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Series III}, issn = {0031-8019}, mrclass = {03G30 (00A30 03A05 18B99)}, mrnumber = {MR1406758 (99c:03106)}, mrreviewer = {Colin McLarty} } @ARTICLE{ab:bracket-types, author = {Awodey, Steven and Bauer, Andrej}, title = {Propositions as [types]}, journal = {J. Logic Comput.}, year = {2004}, volume = {14}, pages = {447--471}, number = {4}, doi = {10.1093/logcom/14.4.447}, fjournal = {Journal of Logic and Computation}, issn = {0955-792X}, mrclass = {03B15 (03B20 03B45 18C50)}, mrnumber = {MR2081047 (2005d:03015)}, url = {http://dx.doi.org/10.1093/logcom/14.4.447} } % foss-et @ARTICLE{abss:bulletin-announcement, author = {Awodey, Steve and Butz, Carsten and Simpson, Alex and Streicher, Thomas}, title = {Relating first-order set theories and elementary toposes}, journal = {Bull. Symbolic Logic}, year = {2007}, volume = {13}, pages = {340--358}, number = {3}, fjournal = {Bulletin of Symbolic Logic}, issn = {1079-8986}, mrclass = {03G30 (03F50)}, mrnumber = {MR2359910} } % rfosttcoc @UNPUBLISHED{abss:long-version-draft, author = {Steve Awodey and Carsten Butz and Alex Simpson and Thomas Streicher}, title = {Relating first-order set theories, toposes, and categories of classes}, note = {\url{http://www.phil.cmu.edu/projects/ast/Papers/abss.pdf}}, year = {2007} } @article{abss:long-version, title = "Relating first-order set theories, toposes and categories of classes ", journal = "Annals of Pure and Applied Logic ", volume = "165", number = "2", pages = "428 - 502", year = "2014", note = "", issn = "0168-0072", doi = "http://dx.doi.org/10.1016/j.apal.2013.06.004", url = "http://www.sciencedirect.com/science/article/pii/S0168007213000730", author = "Steve Awodey and Carsten Butz and Alex Simpson and Thomas Streicher", keywords = "Intuitionistic set theory", keywords = "Elementary topos", keywords = "Algebraic set theory " } % topsetviacofc @UNPUBLISHED{abss:long-version-early-draft, author = {Steve Awodey and Carsten Butz and Alex Simpson and Thomas Streicher}, title = {Relating topos theory and set theory via categories of classes}, note = {I have a PDF of this\dots}, month = {June}, year = {2003} } % Does categorial ideals, impredicatively @ARTICLE{af:ast-classes, author = {Awodey, S. and Forssell, H.}, title = {Algebraic models of intuitionistic theories of sets and classes}, journal = {Theory Appl. Categ.}, year = {2005/06}, volume = {15}, pages = {No. 5, 147--163 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18B05 (03E70 03F60 03G30 18B25 18C10)}, mrnumber = {MR2210578 (2006k:18004)}, mrreviewer = {Maulik A. Dave} } % Does categorial ideals, predicatively @Article{aw:pred-ast, author = {Steve Awodey and Michael A. Warren}, title = {Predicative algebraic set theory}, journal = {Theory Appl. Categ.}, year = {2005/06}, volume = 15, pages = {No. 1, 1--39 (electronic)}, fjournal = {Theory and Applications of Categories}} % Summarizes+combines Awodey-Forssell and Awodey-Warren @UNPUBLISHED{afw:ast-ideals, author = {Steve Awodey and Henrik Forssell and Michael A. Warren}, title = {Algebraic models of sets and classes in categories of ideals}, note = {Available online at \url{http://www.phil.cmu.edu/projects/ast/}}, year = {2006} } @ARTICLE{aglw:shvs-ast, author = {Awodey, S. and Gambino, N. and Lumsdaine, P. LeF. and Warren, M. A.}, title = {Lawvere-{T}ierney sheaves in algebraic set theory}, journal = {J. Symbolic Logic}, year = {2009}, volume = {74}, pages = {861--890}, number = {3}, coden = {JSYLA6}, fjournal = {Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03G30 (03F50 18Bxx)}, mrnumber = {MR2548465}, url = {http://projecteuclid.org/getRecord?id=euclid.jsl/1245158088} } @UNPUBLISHED{aglw:sheaves-ast, author = {Steve Awodey and Nicola Gambino and Peter LeF. Lumsdaine and Michael A. Warren}, title = {A general construction of internal sheaves in algebraic set theory}, note = {\url{http://www.phil.cmu.edu/projects/ast/}}, year = {2007} } @ARTICLE{aw:htpy-idtype, author = {Steve Awodey and Michael A. Warren}, title = {Homotopy theoretic models of identity types}, eprint = {arXiv:0709.0248}, journal = {Math. Proc. Camb. Phil. Soc.}, pages = {45--55}, year = {2009}, volume = {146}, number = {45} } @PhdThesis{warren:thesis, author = {Michael A. Warren}, title = {Homotopy Theoretic Aspects of Constructive Type Theory}, school = {Carnegie Mellon University}, year = 2008} @MISC{bbdc:pss, author = {John Baez and Toby Bartels and James Dolan and David Corfield}, title = {Property, Structure, and Stuff}, howpublished = {Online at http://math.ucr.edu/home/baez/qg-spring2004/discussion.html}, note = {Accessed Jan 31, 2006} } @UNPUBLISHED{bm:thdual, author = {John Baez and Paul-Andr\'e Melli\'es}, title = {Theories with duality}, note = {In preparation} } @INCOLLECTION{bd:fin-feyn, author = {Baez, John C. and Dolan, James}, title = {From finite sets to {F}eynman diagrams}, booktitle = {Mathematics unlimited---2001 and beyond}, publisher = {Springer}, year = {2001}, pages = {29--50}, address = {Berlin}, mrclass = {18B40 (18Dxx 81T18)}, mrnumber = {MR1852152} } @ARTICLE{bd:hda3, author = {Baez, John C. and Dolan, James}, title = {Higher-dimensional algebra. {III}. {$n$}-categories and the algebra of opetopes}, journal = {Adv. 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Available online at \url{http://www.tac.mta.ca/tac/reprints/articles/12/tr12abs.html}}, fjournal = {Reprints in Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18-02 (03G30 18B25 18C10 18C15)}, mrnumber = {MR2178101} } @ARTICLE{MR1184005, author = {Barr, Michael and Wells, Charles}, title = {On the limitations of sketches}, journal = {Canad. Math. Bull.}, year = {1992}, volume = {35}, pages = {287--294}, number = {3}, coden = {CMBUA3}, fjournal = {Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques}, issn = {0008-4395}, mrclass = {18C10 (18A10)}, mrnumber = {MR1184005 (93i:18009)} } @UNPUBLISHED{bdh:confnets-i, author = {Arthur Bartels and Christopher L. Douglas and Andr\'e Henriques}, title = {Conformal nets {I}: symmetric monoidal 3-categories}, note = {Preprint}, year = {2009} } @ARTICLE{bartle:cor-nets-filters, author = {Bartle, R. G.}, title = {A correction for ``{N}ets and filters in topology''}, journal = {Amer. Math. 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By way of application we obtain an "Ekmann-Hilton" result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras.}, comments = {66 pages. In version 2 we corrected the explicit construction of coequalisers in categories of algebras from section 7 of version 1. The new appendices discuss the background on these transfinite constructions more fully.}, eprint = {0909.4715}, oai2identifier = {0909.4715} } @ARTICLE{MR2072989, author = {Bauer, Andrej and Birkedal, Lars and Scott, Dana S.}, title = {Equilogical spaces}, journal = {Theoret. Comput. 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Pure Appl. Logic}, year = {2007}, volume = {146}, pages = {40--59}, number = {1}, coden = {APALD7}, fjournal = {Annals of Pure and Applied Logic}, issn = {0168-0072}, mrclass = {03B15 (03F50 03G30)}, mrnumber = {MR2311163 (2008c:03004)}, mrreviewer = {Nicola Gambino} } @ARTICLE{vdbdb:nonwellfounded, author = {van den Berg, Benno and De Marchi, Federico}, title = {Models of non-well-founded sets via an indexed final coalgebra theorem}, journal = {J. Symbolic Logic}, year = {2007}, volume = {72}, pages = {767--791}, number = {3}, note = {arXiv:math/0508531}, coden = {JSYLA6}, fjournal = {Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03C90 (03E70 03F50 03G30 18A99)}, mrnumber = {MR2354900 (2008j:03053)}, mrreviewer = {Robert S. Lubarsky} } @article{bg:type-wkom, author = {{van den Berg}, Benno and Garner, Richard}, title = {Types are weak $\omega$-groupoids}, volume = {102}, number = {2}, pages = {370-394}, year = {2011}, journal = {Proceedings of the London Mathematical Society} } %doi = {10.1112/plms/pdq026}, %URL = {http://plms.oxfordjournals.org/content/102/2/370.abstract}, %eprint = {http://plms.oxfordjournals.org/content/102/2/370.full.pdf+html}, @UNPUBLISHED{vdbm:pred-iii-shvs, author = {Benno van den Berg and Ieke Moerdijk}, title = {Aspects of predicative algebraic set theory {III}: {S}heaves}, year = {2009}, eprint = {arXiv:0912.1242} } @UNPUBLISHED{vdbm:pred-ii-realiz, author = {Benno van den Berg and Ieke Moerdijk}, title = {Aspects of predicative algebraic set theory {II}: {R}ealizability}, year = {2008}, eprint = {arXiv:0801.2305} } @UNPUBLISHED{vdbm:pred-i-exact, author = {Benno van den Berg and Ieke Moerdijk}, title = {Aspects of predicative algebraic set theory {I}: {E}xact completion}, year = {2007}, eprint = {arXiv:0710.3077} } @BOOK{vdb:nsaa, title = {Nonstandard Asymptotic Analysis}, publisher = {Springer-Verlag}, year = {1987}, editor = {A. 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Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, 06108 Nice, France}, title = {On an extension of the notion of {R}eedy category}, journal = {Mathematische Zeitschrift}, publisher = {Springer Berlin / Heidelberg}, keyword = {Mathematics and Statistics}, pages = {977-1004}, volume = {269}, issue = {3}, year = {2011}, eprint = {arXiv:0809.3341} } % issn = {0025-5874}, % url = {http://dx.doi.org/10.1007/s00209-010-0770-x}, % note = {10.1007/s00209-010-0770-x}, @INCOLLECTION{bm:res-opd, author = {Berger, Clemens and Moerdijk, Ieke}, title = {Resolution of coloured operads and rectification of homotopy algebras}, booktitle = {Categories in algebra, geometry and mathematical physics}, publisher = {Amer. Math. Soc.}, year = {2007}, volume = {431}, series = {Contemp. 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Gonshor} } @INCOLLECTION{day:closed, author = {Day, Brian}, title = {On closed categories of functors}, booktitle = {Reports of the Midwest Category Seminar, IV}, publisher = {Springer}, year = {1970}, series = {Lecture Notes in Mathematics, Vol. 137}, pages = {1--38}, address = {Berlin}, mrclass = {18.10}, mrnumber = {MR0272852 (42 \#7733)}, mrreviewer = {J. F. Kennison} } @ARTICLE{dms:antipodes, author = {Day, Brian and McCrudden, Paddy and Street, Ross}, title = {Dualizations and antipodes}, journal = {Appl. Categ. Structures}, year = {2003}, volume = {11}, pages = {229--260}, number = {3}, coden = {ACASE6}, fjournal = {Applied Categorical Structures. A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science}, issn = {0927-2852}, mrclass = {18D05 (16W30 18D10 18D20)}, mrnumber = {MR1990034 (2004b:18013)} } @ARTICLE{dp:frob-monoidal, author = {Day, Brian and Pastro, Craig}, title = {Note on {F}robenius monoidal functors}, journal = {New York J. Math.}, year = {2008}, volume = {14}, pages = {733--742}, note = {arXiv:0801.4107}, fjournal = {New York Journal of Mathematics}, issn = {1076-9803}, mrclass = {18A22 (18D10)}, mrnumber = {MR2465800 (2009k:18001)}, mrreviewer = {Giordano Favi} } @ARTICLE{ds:quantum, author = {Brian Day and Ross Street}, title = {Quantum categories, star autonomy, and quantum groupoids}, year = {2007}, abstract = {A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. We define the term "quantum category". The definition of antipode for a bialgebroid is less resolved in the literature. Our suggestion is that the kind of dualization occurring in Barr's star-autonomous categories is more suitable than autonomy (= compactness = rigidity). This leads to our definition of quantum groupoid intended as a "Hopf algebra with several objects".}, comments = {41 pages, PDF file based on MacWrite document This revised version corrects some duality mistakes in the last three sections}, eprint = {math/0301209}, oai2identifier = {math/0301209} } @INCOLLECTION{ds:lmpo-conv, author = {Day, Brian and Street, Ross}, title = {Lax monoids, pseudo-operads, and convolution}, booktitle = {Diagrammatic morphisms and applications ({S}an {F}rancisco, {CA}, 2000)}, publisher = {Amer. Math. Soc.}, year = {2003}, volume = {318}, series = {Contemp. 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(3)}, year = {1990}, volume = {60}, pages = {1--36}, number = {1}, coden = {PLMTAL}, doi = {10.1112/plms/s3-60.1.1}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, issn = {0024-6115}, mrclass = {18B25 (03G30 18B30 18D30)}, mrnumber = {MR1023803 (90k:18004)}, mrreviewer = {Ieke Moerdijk}, url = {http://dx.doi.org/10.1112/plms/s3-60.1.1} } @ARTICLE{hp:pscom-mnds, author = {Hyland, Martin and Power, John}, title = {Pseudo-commutative monads and pseudo-closed 2-categories}, journal = {J. Pure Appl. Algebra}, year = {2002}, volume = {175}, pages = {141--185}, number = {1-3}, note = {Special volume celebrating the 70th birthday of Professor Max Kelly}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05 (18C15 18D15)}, mrnumber = {MR1935977 (2004b:18014)}, mrreviewer = {Graham J. Ellis} } @ARTICLE{hyman:m-spaces, author = {Hyman, D. 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Johnstone}, number = {43}, series = {Oxford Logic Guides} } @BOOK{ptj:elephant2, title = {Sketches of an Elephant: A Topos Theory Compendium: Volume 2}, publisher = {Oxford Science Publications}, year = {2002}, author = {Peter T. Johnstone}, number = {43}, series = {Oxford Logic Guides} } @ARTICLE{ptj:fib-pprod, author = {Johnstone, Peter T.}, title = {Fibrations and partial products in a {$2$}-category}, journal = {Appl. Categ. Structures}, year = {1993}, volume = {1}, pages = {141--179}, number = {2}, coden = {ACASE6}, fjournal = {Applied Categorical Structures. 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Bunge} } @ARTICLE{ptj:topological-topos, author = {Johnstone, Peter T.}, title = {On a topological topos}, journal = {Proc. London Math. Soc. (3)}, year = {1979}, volume = {38}, pages = {237--271}, number = {2}, coden = {PLMTAL}, fjournal = {Proceedings of the London Mathematical Society. Third Series}, } @BOOK{ptj:topos-theory, title = {Topos theory}, publisher = {Academic Press [Harcourt Brace Jovanovich Publishers]}, year = {1977}, author = {Johnstone, Peter T.}, pages = {xxiii+367}, address = {London}, note = {London Mathematical Society Monographs, Vol. 10}, isbn = {0-12-387850-0}, mrclass = {18B99 (02K10 18A15 18C99)}, mrnumber = {MR0470019 (57 \#9791)}, mrreviewer = {Marta C. Bunge} } @ARTICLE{ptj:adjt-lifting, author = {Johnstone, Peter T.}, title = {Adjoint lifting theorems for categories of algebras}, journal = {Bull. London Math. Soc.}, year = {1975}, volume = {7}, pages = {294--297}, number = {3}, fjournal = {The Bulletin of the London Mathematical Society}, issn = {0024-6093}, mrclass = {18C10 (02D99)}, mrnumber = {MR0390018 (52 \#10845)}, mrreviewer = {C. J. Mikkelsen} } @INCOLLECTION{jw:at-toposes, author = {Johnstone, Peter T. and Wraith, Gavin C.}, title = {Algebraic theories in toposes}, booktitle = {Indexed categories and their applications}, publisher = {Springer}, year = {1978}, volume = {661}, series = {Lecture Notes in Math.}, pages = {141--242}, address = {Berlin}, mrclass = {18B25 (18C10)}, mrnumber = {MR514195 (81f:18019)} } @UNPUBLISHED{joyal:quasi, author = {A. Joyal}, title = {The theory of quasi-categories}, note = {In preparation} } @Unpublished{joyal:logoi, author = {Andre Joyal}, title = {Notes on logoi}, note = {\url{http://www.math.uchicago.edu/~may/IMA/JOYAL/Joyal.pdf}}, year = 2008} @MISC{joyal:fields, author = {Andr\'e Joyal}, title = {From quasi-categories to higher categories}, howpublished = {Talk at the Fields Institute Workshop on higher categories and their applications}, month = {Jan}, year = {2007} } @ARTICLE{joyal:q_kan, author = {A. Joyal}, title = {Quasi-categories and {K}an complexes}, journal = {Journal of Pure and Applied Algebra}, year = {2002}, volume = {175}, pages = {207-222} } @UNPUBLISHED{joyal:unbdd-cxs-modelstr, author = {A.~Joyal}, title = {Letter to {A}.~{G}rothendieck}, year = {1984} } @ARTICLE{joyal:species, author = {Joyal, Andr{\'e}}, title = {Une th\'eorie combinatoire des s\'eries formelles}, journal = {Adv. in Math.}, year = {1981}, volume = {42}, pages = {1--82}, number = {1}, coden = {ADMTA4}, fjournal = {Advances in Mathematics}, issn = {0001-8708}, mrclass = {05A99 (18B99 26B10)}, mrnumber = {MR633783 (84d:05025)} } @ARTICLE{joyal:games, author = {Andr\'{e} Joyal}, title = {Remarques sur la Th\'{e}orie des Jeux \`{a} deus personnes}, journal = {Gazette des sciences math\'{e}matiques du Qu\'{e}bec}, year = {1977}, volume = {1}, number = {4}, note = {English translation available at \url{http://www.ma.man.ac.uk/~rhouston/Joyal-games.ps}} } @INCOLLECTION{jk:weak-units, author = {Joyal, Andr{\'e} and Kock, Joachim}, title = {Weak units and homotopy 3-types}, booktitle = {Categories in algebra, geometry and mathematical physics}, publisher = {Amer. Math. Soc.}, year = {2007}, volume = {431}, series = {Contemp. Math.}, pages = {257--276}, address = {Providence, RI}, mrclass = {18D05 (18D10 55P99)}, mrnumber = {MR2342833 (2008j:18005)}, mrreviewer = {Fernando Muro} } @BOOK{jm:ast, title = {Algebraic set theory}, publisher = {Cambridge University Press}, year = {1995}, author = {Joyal, A. and Moerdijk, I.}, volume = {220}, pages = {viii+123}, series = {London Mathematical Society Lecture Note Series}, address = {Cambridge}, isbn = {0-521-55830-1}, mrclass = {03E70 (03-02 03C90 03F55 03G25 04A10)}, mrnumber = {MR1368403 (96k:03127)}, mrreviewer = {Ioan Tofan} } @ARTICLE{jm:open-maps, author = {Joyal, A. and Moerdijk, I.}, title = {A completeness theorem for open maps}, journal = {Ann. Pure Appl. Logic}, year = {1994}, volume = {70}, pages = {51--86}, number = {1}, coden = {APALD7}, fjournal = {Annals of Pure and Applied Logic}, issn = {0168-0072}, mrclass = {03G30 (54C10)}, mrnumber = {MR1303663 (95j:03104)}, mrreviewer = {Peter Johnstone} } @ARTICLE{jnw:bisim2, author = {Joyal, Andr{\'e} and Nielsen, Mogens and Winskel, Glynn}, title = {Bisimulation from open maps}, journal = {Inform. and Comput.}, year = {1996}, volume = {127}, pages = {164--185}, number = {2}, note = {Special issue dedicated to Paris Christos Kanellakis}, fjournal = {Information and Computation}, issn = {0890-5401}, mrclass = {68Q10 (18B25 68Q05 68Q55 68Q60)}, mrnumber = {MR1407994 (98f:68082)} } @INCOLLECTION{jnw:bisim, author = {Joyal, Andr{\'e} and Nielsen, Mogens and Winskel, Glynn}, title = {Bisimulation and open maps}, booktitle = {Eighth {A}nnual {IEEE} {S}ymposium on {L}ogic in {C}omputer {S}cience ({M}ontreal, {PQ}, 1993)}, publisher = {IEEE Comput. Soc. Press}, year = {1993}, pages = {418--427}, address = {Los Alamitos, CA}, mrclass = {68Q10}, mrnumber = {MR1238300 (94i:68082)} } @ARTICLE{js:brd-tensor, author = {Joyal, Andr{\'e} and Street, Ross}, title = {Braided tensor categories}, journal = {Adv. Math.}, year = {1993}, volume = {102}, pages = {20--78}, number = {1}, coden = {ADMTA4}, fjournal = {Advances in Mathematics}, issn = {0001-8708}, mrclass = {18D10 (19D23 20G05)}, mrnumber = {MR1250465 (94m:18008)}, mrreviewer = {Daniel Conduch{\'e}} } @ARTICLE{js:geom-tenscalc-i, author = {Joyal, Andr{\'e} and Street, Ross}, title = {The geometry of tensor calculus. {I}}, journal = {Adv. Math.}, year = {1991}, volume = {88}, pages = {55--112}, number = {1}, coden = {ADMTA4}, fjournal = {Advances in Mathematics}, issn = {0001-8708}, mrclass = {18G99 (57M05)}, mrnumber = {MR1113284 (92d:18011)}, mrreviewer = {Louis H. Kauffman} } @Unpublished{js:geom-tenscalc-ii, author = {Joyal, Andr{\'e} and Street, Ross}, title = {The geometry of tensor calculus. {II}}, note = {Draft available at \url{http://www.math.mq.edu.au/~street/GTCII.pdf}}} @Unpublished{js:pdta, author = {Joyal, Andr{\'e} and Street, Ross}, title = {Planar diagrams and tensor algebra}, note = {Draft available at \url{http://www.math.mq.edu.au/~street/PlanarDiags.pdf}}} @ARTICLE{jsv:traced-moncat, author = {Joyal, Andr{\'e} and Street, Ross and Verity, Dominic}, title = {Traced monoidal categories}, journal = {Math. Proc. Cambridge Philos. Soc.}, year = {1996}, volume = {119}, pages = {447--468}, number = {3}, coden = {MPCPCO}, fjournal = {Mathematical Proceedings of the Cambridge Philosophical Society}, issn = {0305-0041}, mrclass = {18D10 (03B70 19D23 57M25 68Q55)}, mrnumber = {MR1357057 (96m:18014)}, mrreviewer = {R. Gylys} } @INCOLLECTION{jt:strong-stacks, author = {Joyal, Andr{\'e} and Tierney, Myles}, title = {Strong stacks and classifying spaces}, booktitle = {Category theory (Como, 1990)}, publisher = {Springer}, year = {1991}, volume = {1488}, series = {Lecture Notes in Math.}, pages = {213--236}, address = {Berlin}, mrclass = {18G55 (18B25)}, mrnumber = {MR1173014 (93h:18019)}, mrreviewer = {Kimmo I. Rosenthal} } @ARTICLE{jt:galois, author = {Joyal, Andr{\'e} and Tierney, Myles}, title = {An extension of the {G}alois theory of {G}rothendieck}, journal = {Mem. Amer. Math. Soc.}, year = {1984}, volume = {51}, pages = {vii+71}, number = {309}, coden = {MAMCAU}, fjournal = {Memoirs of the American Mathematical Society}, issn = {0065-9266}, mrclass = {18B25 (06D20 13B05 14A20 18D15 54A05 54C10)}, mrnumber = {MR756176 (86d:18002)}, mrreviewer = {Peter Johnstone} } @ARTICLE{MR1822840, author = {J{\"u}rjens, Jan}, title = {On a problem of {G}abriel and {U}lmer}, journal = {J. Pure Appl. Algebra}, year = {2001}, volume = {158}, pages = {183--196}, number = {2-3}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18C10 (18A40)}, mrnumber = {MR1822840 (2002c:18003)}, mrreviewer = {Walter Tholen} } @BOOK{kanamori:higher-infinite, title = {The higher infinite}, publisher = {Springer-Verlag}, year = {2003}, author = {Kanamori, Akihiro}, pages = {xxii+536}, series = {Springer Monographs in Mathematics}, address = {Berlin}, edition = {Second}, note = {Large cardinals in set theory from their beginnings}, isbn = {3-540-00384-3}, mrclass = {03E55 (01A55 01A60 03-02 03-03)}, mrnumber = {MR1994835 (2004f:03092)} } @ARTICLE{kv:bm2cat, author = {Kapranov, M. and Voevodsky, V.}, title = {Braided monoidal {$2$}-categories and {M}anin-{S}chechtman higher braid groups}, journal = {J. Pure Appl. Algebra}, year = {1994}, volume = {92}, pages = {241--267}, number = {3}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05 (20F36 57M05)}, mrnumber = {MR1266348 (95a:18006)}, mrreviewer = {J. Stasheff} } @INCOLLECTION{kv:2cat-zam, author = {Kapranov, M. M. and Voevodsky, V. A.}, title = {{$2$}-categories and {Z}amolodchikov tetrahedra equations}, booktitle = {Algebraic groups and their generalizations: quantum and infinite-dimensional methods ({U}niversity {P}ark, {PA}, 1991)}, publisher = {Amer. Math. Soc.}, year = {1994}, volume = {56}, series = {Proc. Sympos. Pure Math.}, pages = {177--259}, address = {Providence, RI}, mrclass = {18D05 (17B37 81R50)}, mrnumber = {MR1278735 (95f:18011)}, mrreviewer = {R. H. Street} } @ARTICLE{bv:infgpd-hotypes, author = {Kapranov, M. M. and Voevodsky, V. A.}, title = {{$\infty$}-groupoids and homotopy types}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle Cat\'eg.}, year = {1991}, volume = {32}, pages = {29--46}, number = {1}, note = {International Category Theory Meeting (Bangor, 1989 and Cambridge, 1990)}, annote = {Appears to be wrong; see arXiv:math/9810059}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {0008-0004}, mrclass = {55P15 (18D05 55U10)}, mrnumber = {MR1130401 (93c:55006)}, mrreviewer = {Ronald Brown} } @ARTICLE{MR866936, author = {Kasangian, S.}, title = {{$B$}-categories and gamuts}, journal = {Diagrammes}, year = {1986}, volume = {15}, pages = {K1--K13}, fjournal = {Diagrammes}, issn = {0224-3911}, mrclass = {18D20 (18B20 18D05 68Q05)}, mrnumber = {MR866936 (88i:18006)}, mrreviewer = {R. H. Street} } @BOOK{ks:shvs-mfds, title = {Sheaves on manifolds}, publisher = {Springer-Verlag}, year = {1990}, author = {Kashiwara, Masaki and Schapira, Pierre}, volume = {292}, pages = {x+512}, series = {Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]}, address = {Berlin}, note = {With a chapter in French by Christian Houzel}, isbn = {3-540-51861-4}, mrclass = {58G07 (18F20 32C38 35A27)}, mrnumber = {MR1299726 (95g:58222)} } @ARTICLE{MR0193608, author = {Kat{\v{e}}tov, M.}, title = {On continuity structures and spaces of mappings}, journal = {Comment. Math. Univ. Carolinae}, year = {1965}, volume = {6}, pages = {257--278}, fjournal = {Commentationes Mathematicae Universitatis Carolinae}, issn = {0010-2628}, mrclass = {54.28}, mrnumber = {MR0193608 (33 \#1826)}, mrreviewer = {D. Bushaw} } @BOOK{kelley:gen-top, title = {General topology}, publisher = {Springer-Verlag}, year = {1975}, author = {Kelley, John L.}, pages = {xiv+298}, address = {New York}, note = {Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.], Graduate Texts in Mathematics, No. 27}, mrclass = {54-XX}, mrnumber = {MR0370454 (51 \#6681)} } @ARTICLE{kelley:convergence, author = {Kelley, J. L.}, title = {Convergence in topology}, journal = {Duke Math. J.}, year = {1950}, volume = {17}, pages = {277--283}, fjournal = {Duke Mathematical Journal}, issn = {0012-7094}, mrclass = {56.0X}, mrnumber = {MR0036982 (12,194f)}, mrreviewer = {C. E. Rickart} } @ARTICLE{kelly:operads, author = {Kelly, G. M.}, title = {On the operads of {J}. {P}. {M}ay}, journal = {Repr. Theory Appl. Categ.}, year = {2005}, pages = {1--13 (electronic)}, number = {13}, fjournal = {Reprints in Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18D50 (18C15 18D10 18D20)}, mrnumber = {MR2177746 (2006f:18005)}, mrreviewer = {Agust{\'{\i}} Roig} } @INCOLLECTION{kelly:club-dt, author = {Kelly, G. M.}, title = {On clubs and data-type constructors}, booktitle = {Applications of categories in computer science ({D}urham, 1991)}, publisher = {Cambridge Univ. Press}, year = {1992}, volume = {177}, series = {London Math. Soc. Lecture Note Ser.}, pages = {163--190}, address = {Cambridge}, mrclass = {68Q55 (18D15)}, mrnumber = {MR1176963 (93j:68120)}, mrreviewer = {Eugenio Moggi} } @ARTICLE{kelly:2limits, author = {G. M. Kelly}, title = {Elementary observations on 2-categorical limits}, journal = {Bull. Austral. Math. Soc}, year = {1989}, volume = {39}, pages = {301--317}, number = {2} } @ARTICLE{kelly:totality, author = {Kelly, G. M.}, title = {A survey of totality for enriched and ordinary categories}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle Cat\'eg.}, year = {1986}, volume = {27}, pages = {109--132}, number = {2}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {0008-0004}, mrclass = {18D20 (18A35 18A40)}, mrnumber = {MR850527 (87k:18009)}, mrreviewer = {Walter Tholen} } @ARTICLE{kelly:enr-lfp, author = {Kelly, G. M.}, title = {Structures defined by finite limits in the enriched context. {I}}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = {1982}, volume = {23}, pages = {3--42}, number = {1}, note = {Third Colloquium on Categories, Part VI (Amiens, 1980)}, coden = {CTGDBR}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle}, issn = {0008-0004}, mrclass = {18D15 (18D20)}, mrnumber = {MR648793 (83h:18007)}, mrreviewer = {Walter Tholen} } @BOOK{kelly:enriched, title = {Basic concepts of enriched category theory}, publisher = {Cambridge University Press}, year = {1982}, author = {G. M. Kelly}, volume = {64}, series = {London Mathematical Society Lecture Note Series}, note = {Also available online in Reprints in Theory and Applications of Categories, No. 10 (2005) pp. 1-136} } @ARTICLE{kelly:transfinite-add, author = {Kelly, G. M.}, title = {Two addenda: ``{A} unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves and so on'' [{B}ull. {A}ustral. {M}ath. {S}oc. {\bf 22} (1980), no. 1, 1--83;\ {MR} 82h:18003]}, journal = {Bull. Austral. Math. Soc.}, year = {1982}, volume = {26}, pages = {221--237}, number = {2}, coden = {ALNBAB}, fjournal = {Bulletin of the Australian Mathematical Society}, issn = {0004-9727}, mrclass = {18C15 (18A40)}, mrnumber = {MR683654 (84a:18011)}, mrreviewer = {V{\'a}clav Koubek} } @ARTICLE{kelly:transfinite, author = {Kelly, G. M.}, title = {A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on}, journal = {Bull. Austral. Math. Soc.}, year = {1980}, volume = {22}, pages = {1--83}, number = {1}, coden = {ALNBAB}, fjournal = {Bulletin of the Australian Mathematical Society}, issn = {0004-9727}, mrclass = {18C15 (18A40)}, mrnumber = {MR589937 (82h:18003)}, mrreviewer = {V{\'a}clav Koubek} } @Misc{nlab:transfinite, author = {{nLab authors}}, title = {Transfinite construction of free algebras}, howpublished = {\url{https://ncatlab.org/nlab/show/transfinite+construction+of+free+algebras}}} @ARTICLE{MR578566, author = {Kelly, G. M.}, title = {Examples of nonmonadic structures on categories}, journal = {J. Pure Appl. Algebra}, year = {1980}, volume = {18}, pages = {59--66}, number = {1}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D15 (18C20)}, mrnumber = {MR578566 (82e:18013)}, mrreviewer = {Walter Tholen} } @INCOLLECTION{kelly:club-doc, author = {Kelly, G. M.}, title = {On clubs and doctrines}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, publisher = {Springer}, year = {1974}, pages = {181--256. Lecture Notes in Math., Vol. 420}, address = {Berlin}, } @INCOLLECTION{kelly:coh-lax, author = {Kelly, G. M.}, title = {Coherence theorems for lax algebras and for distributive laws}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, publisher = {Springer}, year = {1974}, pages = {281--375. Lecture Notes in Math., Vol. 420}, address = {Berlin}, mrclass = {18D05}, mrnumber = {MR0364394 (51 \#648)}, mrreviewer = {M. L. Laplaza} } @INCOLLECTION{kelly:doc-adjn, author = {Kelly, G. M.}, title = {Doctrinal adjunction}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, publisher = {Springer}, year = {1974}, pages = {257--280. Lecture Notes in Math., Vol. 420}, address = {Berlin}, mrclass = {18D99}, mrnumber = {MR0360749 (50 \#13196)}, mrreviewer = {A. Shafaat} } @INCOLLECTION{kelly:abst-coh, author = {Kelly, G. M.}, title = {An abstract approach to coherence}, booktitle = {Coherence in categories}, publisher = {Springer}, year = {1972}, pages = {106--147. Lecture Notes in Math., Vol. 281}, address = {Berlin}, mrclass = {18D15}, mrnumber = {MR0340372 (49 \#5127)}, mrreviewer = {M. L. Laplaza} } @INCOLLECTION{kelly:mv-funct-calc, author = {Kelly, G. M.}, title = {Many-variable functorial calculus. {I}}, booktitle = {Coherence in categories}, publisher = {Springer}, year = {1972}, pages = {66--105. Lecture Notes in Math., Vol. 281}, address = {Berlin}, mrclass = {18D15}, mrnumber = {MR0340371 (49 \#5126)}, mrreviewer = {M. L. Laplaza} } @INCOLLECTION{kelly:cutelim, author = {Kelly, G. M.}, title = {A cut-elimination theorem}, booktitle = {Coherence in categories}, publisher = {Springer}, year = {1972}, pages = {196--213. Lecture Notes in Math., Vol. 281}, address = {Berlin}, } @ARTICLE{kelly:mono-epi-pb, author = {Kelly, G. M.}, title = {Monomorphisms, epimorphisms, and pull-backs}, journal = {J. Austral. Math. Soc.}, year = {1969}, volume = {9}, pages = {124--142}, fjournal = {Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics}, issn = {0263-6115}, mrclass = {18.10}, mrnumber = {MR0240161 (39 \#1515)}, mrreviewer = {Y. C. Wu} } @ARTICLE{MR0182649, author = {Kelly, G. M.}, title = {On {M}ac{L}ane's conditions for coherence of natural associativities, commutativities, etc}, journal = {J. Algebra}, year = {1964}, volume = {1}, pages = {397--402}, fjournal = {Journal of Algebra}, issn = {0021-8693}, mrclass = {18.10}, mrnumber = {MR0182649 (32 \#132)}, mrreviewer = {M. Auslander} } @ARTICLE{kk:large-lim, author = {Kelly, G. M. and Koubek, V.}, title = {The large limits that all good categories admit}, journal = {J. Pure Appl. Algebra}, year = {1981}, volume = {22}, pages = {253--263}, number = {3}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18A20 (18A35)}, mrnumber = {MR629334 (82j:18002)}, mrreviewer = {M. Barr} } @ARTICLE{kl:vcat-locpres, author = {Kelly, G. M. and Lack, Stephen}, title = {{$\mathscr{V}$}-{C}at is locally presentable or locally bounded if {$\mathscr{V}$} is so}, journal = {Theory Appl. Categ.}, year = {2001}, volume = {8}, pages = {555--575 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18C35 (18D20)}, mrnumber = {MR1870617 (2002k:18006)}, mrreviewer = {Kimmo I. Rosenthal} } @ARTICLE{kl:property-like, author = {G. M. Kelly and Stephen Lack}, title = {On property-like structures}, journal = {Theory Appl. Categ.}, year = {1997}, volume = {3}, pages = {213--250}, number = {9} } @ARTICLE{kl:strongly-finitary, author = {Kelly, G. M. and Lack, Stephen}, title = {Finite-product-preserving functors, {K}an extensions and strongly-finitary {$2$}-monads}, journal = {Appl. Categ. Structures}, year = {1993}, volume = {1}, pages = {85--94}, number = {1}, coden = {ACASE6}, fjournal = {Applied Categorical Structures. A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science}, issn = {0927-2852}, mrclass = {18C15 (18A40 18D20)}, mrnumber = {MR1245794 (94k:18009)} } @ARTICLE{klw:refl-coinv, author = {Kelly, G. M. and Lack, Stephen and Walters, R.F.C.}, title = {Coinverters and categories of fractions for categories with structure}, journal = {Appl. Categ. Structures}, year = {1993}, volume = {1}, pages = {95--102}, number = {1}, coden = {ACASE6}, doi = {10.1007/BF00872988}, fjournal = {Applied Categorical Structures. A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science}, issn = {0927-2852}, mrclass = {18D99 (18A30 18A35)}, mrnumber = {MR1245795 (94k:18012)}, url = {http://dx.doi.org/10.1007/BF00872988} } @ARTICLE{kl:cpt, author = {G. M. Kelly and M. L. Laplaza}, title = {Coherence for compact closed categories}, journal = {J. Pure Appl. Algebra}, year = {1980}, volume = {19}, pages = {193--213} } @ARTICLE{kp:note-closure, author = {Kelly, G. M. and Par{\'e}, Robert}, title = {A note on the {M}. {H}. {A}lbert-{G}. {M}. {K}elly paper: ``{T}he closure of a class of colimits'' [{J}. {P}ure {A}ppl.\ {A}lgebra {\bf 51} (1988), no.\ 1, 1--17]}, journal = {J. Pure Appl. Algebra}, year = {1988}, volume = {51}, pages = {19--25}, number = {1-2}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18A35 (18A30 18D15)}, mrnumber = {MR941886 (89g:18003b)}, mrreviewer = {Walter Tholen} } @ARTICLE{finitary-monads, author = {G. M. Kelly and A. J. Power}, title = {Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads}, journal = {J. Pure Appl. Algebra}, year = {1993}, volume = {89}, pages = {163--179}, number = {1-2} } @ARTICLE{MR2211425, author = {Kelly, G. M. and Schmitt, V.}, title = {Notes on enriched categories with colimits of some class}, journal = {Theory Appl. Categ.}, year = {2005}, volume = {14}, pages = {no. 17, 399--423 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18A35 (18C35 18D20)}, mrnumber = {MR2211425 (2006k:18003)}, mrreviewer = {Stephen Lack} } @INPROCEEDINGS{ks:r2cats, author = {G. M. Kelly and Ross Street}, title = {Review of the elements of $2$-categories}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, year = {1974}, volume = {420}, series = {Lecture Notes in Math.}, pages = {75--103}, publisher = {Springer, Berlin} } @ARTICLE{2sided-enrichment, author = {Kelly, Max and Labella, Anna and Schmitt, Vincent and Street, Ross}, title = {Categories enriched on two sides}, journal = {J. Pure Appl. Algebra}, year = {2002}, volume = {168}, pages = {53--98}, number = {1}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05 (18D20)}, mrnumber = {MR1879931 (2003f:18006)}, mrreviewer = {Marta C. Bunge} } @ARTICLE{kennedy:nets-filters, author = {Kennedy, Maurice}, title = {The connection between nets and filters}, journal = {Irish Math. Soc. Newslett.}, year = {1984}, pages = {24--28}, number = {11}, fjournal = {Irish Mathematical Society Newsletter}, mrclass = {54A20 (03E25)}, mrnumber = {MR762005 (86a:54002)}, mrreviewer = {P. Kratochv{\'{\i}}l} } @ARTICLE{kp:lax-nat-enr, author = {Kinoshita, Yoshiki and Power, John}, title = {Lax naturality through enrichment}, journal = {J. Pure Appl. Algebra}, year = {1996}, volume = {112}, pages = {53--72}, number = {1}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18C15 (18D10)}, mrnumber = {MR1402396 (98f:18010)} } @ARTICLE{kisynski:conv-typel, author = {Kisy{\'n}ski, J.}, title = {Convergence du type {${\cal L}$}}, journal = {Colloq. Math.}, year = {1959/1960}, volume = {7}, pages = {205--211}, fjournal = {Colloquium Mathematicum}, issn = {0010-1354}, mrclass = {54.22}, mrnumber = {MR0123287 (23 \#A615)}, mrreviewer = {P. Dedecker} } @UNPUBLISHED{kock:postulated, author = {Anders Kock}, title = {Postulated colimits and left exactness of {K}an-extensions}, note = {Aarhus Preprint 1989/90 no. 9, Retyped in TeX in the fall of 2003. Available at \url{http://home.imf.au.dk/kock/}}, year = 1989 } @ARTICLE{kock:kzmonads, author = {Kock, Anders}, title = {Monads for which structures are adjoint to units}, journal = {J. Pure Appl. Algebra}, year = {1995}, volume = {104}, pages = {41--59}, number = {1}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05 (18A35 18C15)}, mrnumber = {MR1359690 (96k:18009)}, mrreviewer = {R. H. Street} } @BOOK{kock:sdg, title = {Synthetic differential geometry}, publisher = {Cambridge University Press}, year = {1981}, author = {Kock, Anders}, volume = {51}, pages = {vi+311}, series = {London Mathematical Society Lecture Note Series}, address = {Cambridge}, isbn = {0-521-24138-3}, mrclass = {51K10 (03F55 03G30 18F15 58A05)}, mrnumber = {MR649622 (83f:51023)}, mrreviewer = {Gavin Wraith} } @ARTICLE{kock:strfunc-monmnd, author = {Kock, Anders}, title = {Strong functors and monoidal monads}, journal = {Arch. Math. (Basel)}, year = {1972}, volume = {23}, pages = {113--120}, fjournal = {Archiv der Mathematik}, issn = {0003-889X}, mrclass = {18D10}, mrnumber = {MR0304456 (46 \#3591)}, mrreviewer = {J. R. Isbell} } @ARTICLE{kock:bilin-ccmnd, author = {Kock, Anders}, title = {Bilinearity and {C}artesian closed monads}, journal = {Math. Scand.}, year = {1971}, volume = {29}, pages = {161--174 (1972)}, fjournal = {Mathematica Scandinavica}, issn = {0025-5521}, mrclass = {18D15}, mrnumber = {MR0310038 (46 \#9141)}, mrreviewer = {J. R. Isbell} } @ARTICLE{kock:cc-commnd, author = {Kock, Anders}, title = {Closed categories generated by commutative monads}, journal = {J. Austral. Math. Soc.}, year = {1971}, volume = {12}, pages = {405--424}, fjournal = {Australian Mathematical Society. Journal. Series A. Pure Mathematics and Statistics}, issn = {0263-6115}, mrclass = {18D15}, mrnumber = {MR0296129 (45 \#5190)}, mrreviewer = {J. R. Isbell} } @ARTICLE{kock:dbldual-mnd, author = {Kock, Anders}, title = {On double dualization monads}, journal = {Math. Scand.}, year = {1970}, volume = {27}, pages = {151--165 (1971)}, fjournal = {Mathematica Scandinavica}, issn = {0025-5521}, mrclass = {18C15}, mrnumber = {MR0347935 (50 \#435)}, mrreviewer = {G. M. Kelly} } @ARTICLE{kock:mnd-smcc, author = {Kock, Anders}, title = {Monads on symmetric monoidal closed categories}, journal = {Arch. Math. (Basel)}, year = {1970}, volume = {21}, pages = {1--10}, fjournal = {Archiv der Mathematik}, issn = {0003-889X}, mrclass = {18.10}, mrnumber = {MR0260825 (41 \#5446)}, mrreviewer = {Y. C. Wu} } @BOOK{MR0280562, title = {Strong functors and monoidal monads}, publisher = {Matematisk Institut, Aarhus Universitet, Aarhus}, year = {1970}, author = {Kock, Anders}, pages = {i+20}, series = {Various Publication Series, No. 11}, mrclass = {18.10}, mrnumber = {MR0280562 (43 \#6282)}, mrreviewer = {M. Tierney} } @article {kock:weakids, AUTHOR = {Kock, Joachim}, TITLE = {Weak identity arrows in higher categories}, JOURNAL = {IMRP Int. Math. Res. Pap.}, FJOURNAL = {IMRP. International Mathematics Research Papers}, YEAR = {2006}, PAGES = {69163, 1--54}, ISSN = {1687-3017}, MRCLASS = {18D05}, MRNUMBER = {2210659 (2006k:18010)}, MRREVIEWER = {Fernando Muro}, eprint = {arXiv:math/0507116} } @BOOK{jk:frob-2dtqft, title = {Frobenius algebras and 2{D} topological quantum field theories}, publisher = {Cambridge University Press}, year = {2004}, author = {Kock, Joachim}, volume = {59}, pages = {xiv+240}, series = {London Mathematical Society Student Texts}, address = {Cambridge}, isbn = {0-521-83267-5; 0-521-54031-3}, mrclass = {57R56 (16L60 18D10 53D45 81T45)}, mrnumber = {MR2037238 (2005a:57028)}, mrreviewer = {Lowell Abrams} } @ARTICLE{koslowski:polycats, author = {Koslowski, J{\"u}rgen}, title = {A monadic approach to polycategories}, journal = {Theory Appl. Categ.}, year = {2005}, volume = {14}, pages = {No. 7, 125--156 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18C15 (18D05)}, mrnumber = {MR2156193 (2006d:18003)}, mrreviewer = {Steve Awodey} } @ARTICLE{kgvo:ast-eff, author = {Kouwenhoven-Gentil, Claire and van Oosten, Jaap}, title = {Algebraic set theory and the effective topos}, journal = {J. 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Algebra}, year = {1980}, volume = {19}, pages = {215--257}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {03G30 (03F50 18B25)}, mrnumber = {MR593255 (82b:03112)}, mrreviewer = {Andreas Blass} } @ARTICLE{laplaza:emb-closed, author = {Laplaza, Miguel L.}, title = {Embedding of closed categories into monoidal closed categories}, journal = {Trans. Amer. Math. Soc.}, year = {1977}, volume = {233}, pages = {85--91}, fjournal = {Transactions of the American Mathematical Society}, issn = {0002-9947}, mrclass = {18D15}, mrnumber = {MR0480686 (58 \#842)}, mrreviewer = {E. G. Manes} } @BOOK{lavendhomme:sdg, title = {Basic concepts of synthetic differential geometry}, publisher = {Kluwer Academic Publishers Group}, year = {1996}, author = {Lavendhomme, Ren{\'e}}, volume = {13}, pages = {xvi+320}, series = {Kluwer Texts in the Mathematical Sciences}, address = {Dordrecht}, note = {Translated from the 1987 French original, Revised by the author}, isbn = {0-7923-3941-X}, mrclass = {58A03 (51K10 53-01)}, mrnumber = {MR1385464 (98e:58008)}, mrreviewer = {Maria H. Papatriantafillou} } @ARTICLE{lawvere:adjointness, author = {Lawvere, F. William}, title = {Adjointness in foundations}, journal = {Repr. Theory Appl. Categ.}, year = {2006}, pages = {1--16 (electronic)}, number = {16}, note = {Reprinted from Dialectica {\bf 23} (1969)}, fjournal = {Reprints in Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18B25 (00A30 18A15 18A40 18B30 55U40)}, mrnumber = {MR2223032 (2007h:18004)}, mrreviewer = {Steve Awodey} } @ARTICLE{lawvere:etcs-long, author = {Lawvere, F. William}, title = {An elementary theory of the category of sets (long version) with commentary}, journal = {Repr. Theory Appl. Categ.}, year = {2005}, pages = {1--35 (electronic)}, volume = {11}, note = {Reprinted and expanded from Proc. Nat. Acad. Sci. U.S.A. {\bf 52} (1964), With comments by the author and Colin McLarty}, fjournal = {Reprints in Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {03A05 (00B60 03E99 18B05)}, mrnumber = {MR2177727 (2006g:03009)} } @ARTICLE{lawvere:fndapp, author = {Lawvere, F. 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Pure Math., Vol. XVII, New York, 1968)}, publisher = {Amer. Math. Soc.}, year = {1970}, pages = {1--14}, address = {Providence, R.I.}, mrclass = {18.10}, mrnumber = {MR0257175 (41 \#1829)}, mrreviewer = {H. Gonshor} } @INCOLLECTION{lawvere:catofcats, author = {Lawvere, F. William}, title = {The category of categories as a foundation for mathematics}, booktitle = {Proc. Conf. Categorical Algebra (La Jolla, Calif., 1965)}, publisher = {Springer}, year = {1966}, pages = {1--20}, address = {New York}, mrclass = {02.00}, mrnumber = {MR0207517 (34 \#7332)}, mrreviewer = {J. R. Isbell} } @ARTICLE{lawvere:etcs, author = {Lawvere, F. William}, title = {An elementary theory of the category of sets}, journal = {Proc. Nat. Acad. Sci. U.S.A.}, year = {1964}, volume = {52}, pages = {1506--1511}, note = {Reprinted and expanded in {\it Repr. Theory Appl. Categ.} {\bf 11} (2005), with comments by the author and Colin McLarty}, mrclass = {04.99 (18.10)}, mrnumber = {MR0172807 (30 \#3025)}, mrreviewer = {A. Heller} } @ARTICLE{lawvere:functsem, author = {Lawvere, F. William}, title = {Functorial semantics of algebraic theories}, journal = {Proc. Nat. Acad. Sci. U.S.A.}, year = {1963}, volume = {50}, pages = {869--872}, mrclass = {18.10}, mrnumber = {MR0158921 (28 \#2143)}, mrreviewer = {M. Artin} } @ARTICLE{lmv:beck-pseudo, author = {Le Creurer, I. J. and Marmolejo, F. and Vitale, E. M.}, title = {Beck's theorem for pseudo-monads}, journal = {J. Pure Appl. Algebra}, year = {2002}, volume = {173}, pages = {293--313}, number = {3}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18C15 (18D05)}, mrnumber = {MR1916482 (2003f:18004)}, mrreviewer = {Peter Johnstone} } @unpublished{leinster:fc-multicategories, author = {Tom Leinster}, title = {{\bf fc}-multicategories}, year = {2007}, abstract = {fc-multicategories are a very general kind of two-dimensional structure, encompassing bicategories, monoidal categories, double categories and ordinary multicategories. We define them and explain how they provide a natural setting for two familiar categorical ideas. The first is the bimodules construction, traditionally carried out on suitably cocomplete bicategories but perhaps more naturally carried out on fc-multicategories. The second is enrichment: there is a theory of categories enriched in an fc-multicategory, extending the usual theory of enrichment in a monoidal category. We finish by indicating how this work is just the simplest case of a much larger phenomenon.}, comments = {Notes for talk at PSSL 70; 8 pages}, note = {arXiv:math/9903004}, eprint = {math/9903004}, oai2identifier = {math/9903004} } @BOOK{leinster:higher-opds, title = {Higher operads, higher categories}, publisher = {Cambridge University Press}, year = {2004}, author = {Leinster, Tom}, volume = {298}, pages = {xiv+433}, series = {London Mathematical Society Lecture Note Series}, address = {Cambridge}, file = {Higher Operads, Higher Categories 0305049.pdf:Leinster, Tom/Higher Operads, Higher Categories 0305049.pdf:PDF}, isbn = {0-521-53215-9}, mrclass = {18D50 (55P48)}, mrnumber = {MR2094071 (2005h:18030)}, mrreviewer = {R. H. Street} } @ARTICLE{leinster:gen-enr-cats, author = {Leinster, Tom}, title = {Generalized enrichment of categories}, journal = {J. Pure Appl. Algebra}, year = {2002}, volume = {168}, pages = {391--406}, number = {2-3}, note = {Category theory 1999 (Coimbra)}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D20 (18D05 18D10 18D50)}, mrnumber = {MR1887166 (2003a:18008)}, mrreviewer = {H.-J. Hoehnke} } @ARTICLE{leinster:survey, author = {Leinster, Tom}, title = {A survey of definitions of {$n$}-category}, journal = {Theory Appl. Categ.}, year = {2002}, volume = {10}, pages = {1--70 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {18D05 (18D50)}, mrnumber = {MR1883478 (2002i:18008)}, mrreviewer = {Vincent Zoonekynd} } @UNPUBLISHED{leinster:hoalg-opd, author = {Tom Leinster}, title = {Homotopy Algebras for Operads}, note = {arXiv:math/0002180}, year = {2000} } @MISC{leinster:gen-enr-cat-multi, author = {Leinster, Tom}, title = {Generalized enrichment of categories and multicategories}, year = {1999}, eprint = {arXiv:math.CT/9901139}, file = {:Leinster, Tom/Generalized Enrichment for Categories and Multicategories 9901139.pdf:PDF} } @ARTICLE{MR2075334, author = {Leivant, Daniel}, title = {Intrinsic reasoning about functional programs. {II}. {U}nipolar induction and primitive-recursion}, journal = {Theoret. Comput. Sci.}, year = {2004}, volume = {318}, pages = {181--196}, number = {1-2}, coden = {TCSDI}, fjournal = {Theoretical Computer Science}, issn = {0304-3975}, mrclass = {03D80 (03D15 03D20 03F05 68N18 68Q15)}, mrnumber = {MR2075334 (2005f:03064)} } @ARTICLE{MR1879411, author = {Leivant, Daniel}, title = {Intrinsic reasoning about functional programs. {I}. {F}irst order theories}, journal = {Ann. Pure Appl. Logic}, year = {2002}, volume = {114}, pages = {117--153}, number = {1-3}, note = {Commemorative Symposium Dedicated to Anne S. Troelstra (Noordwijkerhout, 1999)}, coden = {APALD7}, fjournal = {Annals of Pure and Applied Logic}, issn = {0168-0072}, mrclass = {03F30 (03D15 03F05 03F20 03F55 68Q15 68W30)}, mrnumber = {MR1879411 (2003b:03082)} } @ARTICLE{MR1673303, author = {Leivant, Daniel}, title = {Ramified recurrence and computational complexity. {III}. {H}igher type recurrence and elementary complexity}, journal = {Ann. Pure Appl. Logic}, year = {1999}, volume = {96}, pages = {209--229}, number = {1-3}, note = {Festschrift on the occasion of Professor Rohit Parikh's 60th birthday}, coden = {APALD7}, fjournal = {Annals of Pure and Applied Logic}, issn = {0168-0072}, mrclass = {03D15 (03F05 03F10 68N18 68Q05 68Q15)}, mrnumber = {MR1673303 (2000b:03148)} } @INCOLLECTION{MR1322281, author = {Leivant, Daniel}, title = {Ramified recurrence and computational complexity. {I}. {W}ord recurrence and poly-time}, booktitle = {Feasible mathematics, II (Ithaca, NY, 1992)}, publisher = {Birkh\"auser Boston}, year = {1995}, volume = {13}, series = {Progr. Comput. Sci. Appl. Logic}, pages = {320--343}, address = {Boston, MA}, mrclass = {03D20 (03D15 08B20 68Q15)}, mrnumber = {MR1322281 (96d:03059)}, mrreviewer = {Gerhard Lischke} } @INCOLLECTION{MR1471248, author = {Leivant, Daniel and Marion, Jean-Yves}, title = {Ramified recurrence and computational complexity. {II}. {S}ubstitution and poly-space}, booktitle = {Computer science logic (Kazimierz, 1994)}, publisher = {Springer}, year = {1995}, volume = {933}, series = {Lecture Notes in Comput. Sci.}, pages = {486--500}, address = {Berlin}, mrclass = {68Q15 (03D15)}, mrnumber = {MR1471248 (98e:68082)} } @ARTICLE{lm:mmmc, author = {Lewis, Jr., L. Gaunce and Mandell, Michael A.}, title = {Modules in monoidal model categories}, journal = {J. Pure Appl. Algebra}, year = {2007}, volume = {210}, pages = {395--421}, number = {2}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18G55 (55P99 55U35)}, mrnumber = {MR2320005}, mrreviewer = {Brooke E. Shipley} } @BOOK{lms:equivariant, title = {Equivariant stable homotopy theory}, publisher = {Springer-Verlag}, year = {1986}, author = {Lewis, Jr., L. G. and May, J. P. and Steinberger, M. and McClure, J. E.}, volume = {1213}, pages = {x+538}, series = {Lecture Notes in Mathematics}, address = {Berlin}, note = {With contributions by J. E. McClure}, isbn = {3-540-16820-6}, mrclass = {55-02 (55Nxx 55Pxx 57S99)}, mrnumber = {MR866482 (88e:55002)}, mrreviewer = {T. tom Dieck} } @MASTERSTHESIS{lietz:fib-gm, author = {Peter Lietz}, title = {A fibrational theory of geometric morphisms}, school = {Technische Universit\"at Darmstadt}, year = {1998}, type = {Diplomarbeit}, note = {Available at \url{http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/lietz.ps.gz}}, annote = {Student of Thomas Streicher. Does lextensive fibrations.} } @ARTICLE{lind:units, author = {John Lind}, title = {Diagram spaces, diagram spectra, and spectra of units}, year = {2009}, month = aug, abstract = {We compare the infinite loop spaces associated to symmetric spectra, orthogonal spectra, and EKMM S-modules. Each of these categories of structured spectra has a corresponding category of structured spaces that receives the infinite loop space functor \Omega^\infty. We prove that these models for spaces are Quillen equivalent and that the infinite loop space functors \Omega^\infty agree. This comparison is then used to show that two different constructions of the spectrum of units gl_1 R of a structured ring spectrum R agree.}, comments = {47 pages}, eprint = {arXiv:0908.1092}, oai2identifier = {0908.1092} } @ARTICLE{lindner:morita-enriched, author = {Lindner, Harald}, title = {Morita equivalences of enriched categories}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = {1974}, volume = {15}, pages = {377--397, 449--450}, number = {4}, note = {Conf\'erences du Colloque sur l'Alg\`ebre des Cat\'egories (Amiens, 1973), III}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {0008-0004}, mrclass = {18D20}, mrnumber = {MR0399209 (53 \#3060)}, mrreviewer = {J. L. Williams} } @ARTICLE{lindstrom:afa-mltt, author = {Lindstr{\"o}m, Ingrid}, title = {A construction of non-well-founded sets within {M}artin-{L}\"of's type theory}, journal = {J. Symbolic Logic}, year = {1989}, volume = {54}, pages = {57--64}, number = {1}, coden = {JSYLA6}, doi = {10.2307/2275015}, fjournal = {The Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03F50}, mrnumber = {MR987322 (90h:03050)}, url = {http://dx.doi.org/10.2307/2275015} } @INPROCEEDINGS{MR621861, author = {Linton, F. E. J.}, title = {Applied functorial semantics. {III}. {C}haracterizing {B}anach conjugate spaces}, booktitle = {Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979)}, year = {1980}, volume = {2}, series = {Contemp. Math.}, pages = {227--240}, address = {Providence, R.I.}, publisher = {Amer. Math. Soc.}, annote = {Banach duals as algebras for the double-dualization monad}, mrclass = {46M15 (18C20 46B10)}, mrnumber = {MR621861 (83d:46084)}, mrreviewer = {J. Sonner} } @INCOLLECTION{MR0288162, author = {Linton, F. E. J.}, title = {The multilinear {Y}oneda lemmas: {T}occata, fugue, and fantasia on themes by {E}ilenberg-{K}elly and {Y}oneda}, booktitle = {Reports of the {M}idwest {C}ategory {S}eminar, {V} ({Z}\"urich, 1970)}, publisher = {Lecture Notes in Mathematics, Vol. 195. Springer, Berlin}, year = {1971}, pages = {209--229}, mrclass = {18.10}, mrnumber = {MR0288162 (44 \#5360)}, mrreviewer = {R. Par{\'e}} } @INCOLLECTION{linton:coeq-alg, author = {Linton, F. E. J.}, title = {Coequalizers in categories of algebras}, booktitle = {Sem. on Triples and Categorical Homology Theory (ETH, Z\"urich, 1966/67)}, publisher = {Springer}, year = {1969}, pages = {75--90}, address = {Berlin}, mrclass = {18.10}, mrnumber = {MR0244341 (39 \#5656)}, mrreviewer = {J. Sonner} } @INCOLLECTION{MR0223534, author = {Linton, F. E. J.}, title = {Functional measure theory}, booktitle = {Functional Analysis (Proc. Conf., Irvine, Calif., 1966)}, publisher = {Academic Press}, year = {1967}, pages = {36--49}, address = {London}, annote = {measures as adjoint to functions}, mrclass = {28.65}, mrnumber = {MR0223534 (36 \#6582)}, mrreviewer = {J. C. Oxtoby} } @ARTICLE{MR651845, author = {Loday, Jean-Louis}, title = {Spaces with finitely many nontrivial homotopy groups}, journal = {J. Pure Appl. 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Mendelson} } @ARTICLE{ml:contrary-stmts, author = {Mac Lane, Saunders}, title = {Contrary statements about mathematics. {C}omment: ``{S}trong statements of analysis'' [{B}ull.\ {L}ondon {M}ath.\ {S}oc. {\bf 32} (2000), no. 5, 513--526; {MR}1767703 (2001h:03102a)] by {A}. {R}. {D}.\ {M}athias}, journal = {Bull. London Math. Soc.}, year = {2000}, volume = {32}, pages = {527}, number = {5}, coden = {LMSBBT}, fjournal = {The Bulletin of the London Mathematical Society}, issn = {0024-6093}, mrclass = {03E65 (03E30 03G30 26A21 54H05)}, mrnumber = {MR1767704 (2001h:03102b)}, mrreviewer = {Julia Y. 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Grattan-Guinness} } @INCOLLECTION{maclane:one-universe, author = {Mac Lane, Saunders}, title = {One universe as a foundation for category theory}, booktitle = {Reports of the Midwest Category Seminar. III}, publisher = {Springer}, year = {1969}, pages = {192--200}, address = {Berlin}, mrclass = {18.10}, mrnumber = {MR0249486 (40 \#2731)}, mrreviewer = {H. Gonshor} } @ARTICLE{maclane:natural-assoc, author = {Mac Lane, Saunders}, title = {Natural associativity and commutativity}, journal = {Rice Univ. Studies}, year = {1963}, volume = {49}, pages = {28--46}, number = {4}, fjournal = {Rice University Studies}, issn = {0035-4996}, mrclass = {18.20}, mrnumber = {MR0170925 (30 \#1160)}, mrreviewer = {D. B. A. Epstein} } @INCOLLECTION{maclane:loc-sm-fdns, author = {Mac Lane, S.}, title = {Locally small categories and the foundations of set theory}, booktitle = {Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959)}, publisher = {Pergamon}, year = {1961}, pages = {25--43}, address = {Oxford}, mrclass = {18.10 (02.00)}, mrnumber = {MR0191941 (33 \#168)}, mrreviewer = {H. Cartan} } @BOOK{mm:shv-gl, title = {Sheaves in geometry and logic: a first introduction to topos theory}, publisher = {Springer-Verlag}, year = {1994}, author = {Mac Lane, Saunders and Moerdijk, Ieke}, series = {Universitext}, address = {New York}, note = {Corrected reprint of the 1992 edition}, } @ARTICLE{mp:coh-bicat, author = {Mac Lane, Saunders and Par{\'e}, Robert}, title = {Coherence for bicategories and indexed categories}, journal = {J. Pure Appl. Algebra}, year = {1985}, volume = {37}, pages = {59--80}, number = {1}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05 (18D30)}, mrnumber = {MR794793 (86k:18003)}, mrreviewer = {W. J. 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Symbolic Logic}, year = {1988}, volume = {53}, pages = {481--511}, number = {2}, coden = {JSYLA6}, fjournal = {The Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03A05 (01A60 03-03 03E30 03E55 04A30)}, mrnumber = {MR947855 (89i:03007)}, mrreviewer = {Mohamed Amer} } @ARTICLE{believing-axioms-ii, author = {Maddy, Penelope}, title = {Believing the axioms. {II}}, journal = {J. Symbolic Logic}, year = {1988}, volume = {53}, pages = {736--764}, number = {3}, coden = {JSYLA6}, fjournal = {The Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03A05 (01A60 03E30 03E55 03E60 04A30)}, mrnumber = {MR960996 (89m:03007)}, mrreviewer = {Mohamed Amer} } @MISC{makkai:comparing, author = {Michael Makkai}, title = {On comparing definitions of weak $n$-category}, howpublished = {Available at \url{http://www.math.mcgill.ca/makkai/}}, month = {August}, year = {2001} } @INCOLLECTION{mak:catfdn, author = {Makkai, M.}, title = {Towards a categorical foundation of mathematics}, booktitle = {Logic Colloquium '95 (Haifa)}, publisher = {Springer}, year = {1998}, volume = {11}, series = {Lecture Notes Logic}, pages = {153--190}, address = {Berlin}, mrclass = {03B15 (00A30 03A05 03G30 18A15 18D05)}, mrnumber = {MR1678360 (2000f:03015)}, mrreviewer = {Peter Johnstone} } @ARTICLE{makkai:avoiding-choice, author = {Makkai, M.}, title = {Avoiding the axiom of choice in general category theory}, journal = {J. Pure Appl. Algebra}, year = {1996}, volume = {108}, pages = {109--173}, number = {2}, coden = {JPAAA2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18A15 (04A25)}, mrnumber = {MR1382246 (97h:18002)}, mrreviewer = {Andreas Blass} } @UNPUBLISHED{makkai:folds, author = {Michael Makkai}, title = {First order logic with dependent sorts, with applications to category theory}, note = {Available at \url{http://www.math.mcgill.ca/makkai/folds/}}, year = {1995} } @BOOK{mp:accessible, title = {Accessible categories: the foundations of categorical model theory}, publisher = {American Mathematical Society}, year = {1989}, author = {Makkai, Michael and Par{\'e}, Robert}, volume = {104}, pages = {viii+176}, series = {Contemporary Mathematics}, address = {Providence, RI}, isbn = {0-8218-5111-X}, mrclass = {03G30 (03C75 03C95 18B25 18C10 18D05 18F10)}, mrnumber = {MR1031717 (91a:03118)}, mrreviewer = {Horst Reichel} } @ARTICLE{mz:3cptd-notcc, author = {Mihaly Makkai and Marek Zawadowski}, title = {The category of 3-computads is not cartesian closed}, journal = {Journal of Pure and Applied Algebra}, year = {2008}, volume = {212}, pages = {2543 - 2546}, number = {11}, doi = {DOI: 10.1016/j.jpaa.2008.04.010}, issn = {0022-4049}, url = {http://www.sciencedirect.com/science/article/B6V0K-4SPSPPV-1/2/c8c53da340a914938bf6c8fcbfb89885} } @ARTICLE{MR0331381, author = {Malraison, Jr., Pierre J.}, title = {Fibrations as triple algebras}, journal = {J. Pure Appl. Algebra}, year = {1973}, volume = {3}, pages = {287--293}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {55F05 (18C15)}, mrnumber = {MR0331381 (48 \#9714)}, mrreviewer = {David Handel} } @ARTICLE{maltsiniotis:traces, author = {Maltsiniotis, G.}, title = {Traces dans les cat\'egories mono\"\i dales, dualit\'e et cat\'egories mono\"\i dales fibr\'ees}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle Cat\'eg.}, year = {1995}, volume = {36}, pages = {195--288}, number = {3}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {0008-0004}, mrclass = {18D10 (57M25)}, mrnumber = {MR1352535 (97d:18007)} } @ARTICLE{mm:eqosp-smod, author = {Mandell, M. A. and May, J. P.}, title = {Equivariant orthogonal spectra and {$S$}-modules}, journal = {Mem. Amer. Math. Soc.}, year = {2002}, volume = {159}, pages = {x+108}, number = {755}, coden = {MAMCAU}, fjournal = {Memoirs of the American Mathematical Society}, issn = {0065-9266}, mrclass = {55P91 (18E30 55P42 55P43 55P48)}, mrnumber = {MR1922205 (2003i:55012)}, mrreviewer = {J. P. C. Greenlees} } @ARTICLE{mmss, author = {Mandell, M. A. and May, J. P. and Schwede, S. and Shipley, B.}, title = {Model categories of diagram spectra}, journal = {Proc. London Math. Soc. (3)}, year = {2001}, volume = {82}, pages = {441--512}, number = {2}, coden = {PLMTAL}, fjournal = {Proceedings of the London Mathematical Society. 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Algebra}, year = {1976}, volume = {8}, pages = {149--181}, number = {2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D05}, mrnumber = {MR0401868 (53 \#5695)}, mrreviewer = {Robert C. Davis} } @INCOLLECTION{street:elem-cosmoi-i, author = {Street, Ross}, title = {Elementary cosmoi. {I}}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, publisher = {Springer}, year = {1974}, pages = {134--180. Lecture Notes in Math., Vol. 420}, address = {Berlin}, mrclass = {18D99}, mrnumber = {MR0354813 (50 \#7290)}, mrreviewer = {H. Gonshor} } @INCOLLECTION{street:fib-yoneda-2cat, author = {Street, Ross}, title = {Fibrations and {Y}oneda's lemma in a {$2$}-category}, booktitle = {Category Seminar (Proc. Sem., Sydney, 1972/1973)}, publisher = {Springer}, year = {1974}, pages = {104--133. Lecture Notes in Math., Vol. 420}, address = {Berlin}, mrclass = {18D05}, mrnumber = {MR0396723 (53 \#585)}, mrreviewer = {A. Pultr} } @ARTICLE{MR0347936, author = {Street, Ross}, title = {Two constructions on lax functors}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = {1972}, volume = {13}, pages = {217--264}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {0008-0004}, mrclass = {18C15}, mrnumber = {MR0347936 (50 \#436)}, mrreviewer = {J. Duskin} } @ARTICLE{street:ftm, author = {Street, Ross}, title = {The formal theory of monads}, journal = {J. Pure Appl. Algebra}, year = {1972}, volume = {2}, pages = {149--168}, number = {2}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18C15}, mrnumber = {MR0299653 (45 \#8701)}, mrreviewer = {F. E. J. Linton} } @ARTICLE{stww:semitop-iii, author = {Street, Ross and Tholen, Walter and Wischnewsky, Manfred and Wolff, Harvey}, title = {Semitopological functors. {III}. {L}ifting of monads and adjoint functors}, journal = {J. Pure Appl. Algebra}, year = {1980}, volume = {16}, pages = {299--314}, number = {3}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18A40}, mrnumber = {MR558494 (81g:18003)}, mrreviewer = {M. Hu{\v{s}}ek} } @ARTICLE{street-walters:yoneda, author = {Street, Ross and Walters, Robert}, title = {Yoneda structures on 2-categories}, journal = {J. Algebra}, year = {1978}, volume = {50}, pages = {350--379}, number = {2}, fjournal = {Journal of Algebra}, issn = {0021-8693}, mrclass = {18D05}, mrnumber = {MR0463261 (57 \#3214)}, mrreviewer = {Symeon Bozapalides} } @ARTICLE{sw:cmprh-fact-funct, author = {Street, Ross and Walters, R.F.C.}, title = {The comprehensive factorization of a functor}, journal = {Bull. Amer. Math. Soc.}, year = {1973}, volume = {79}, pages = {936--941}, mrclass = {18A20 (18D99)}, mrnumber = {MR0346027 (49 \#10753)}, mrreviewer = {A. Pultr} } @UNPUBLISHED{streicher:fibredcats, author = {Thomas Streicher}, title = {Fibred categories \`a la {J}ean {B}\'enabou}, note = {Available at \url{http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/FibLec.pdf.gz}} } @UNPUBLISHED{streicher:moens, author = {Thomas Streicher}, title = {The World's Simplest Proof of Moens' Lemma}, note = {Available at \url{http://www.mathematik.tu-darmstadt.de/~streicher/FIBR/SimplMoens.pdf.gz}}, annote = {All lextensive fibrations arise by Artin gluing from a lex functor} } @INCOLLECTION{streicher:universes, author = {Streicher, Thomas}, title = {Universes in toposes}, booktitle = {From sets and types to topology and analysis}, publisher = {Oxford Univ. Press}, year = {2005}, volume = {48}, series = {Oxford Logic Guides}, pages = {78--90}, address = {Oxford}, mrclass = {03G30 (03F50 03F65 18B25)}, mrnumber = {MR2188637 (2006g:03120)} } @BOOK{ls:infinitesimals, title = {Introduction to the Theory of Infinitesimals}, publisher = {Academic Press}, year = {1976}, author = {K.D. Stroyan and W. A. J. Luxemburg}, series = {Pure and Applied Mathematics} } @ARTICLE{strom:the-htpy-cat, author = {Str{\o}m, Arne}, title = {The homotopy category is a homotopy category}, journal = {Arch. Math. (Basel)}, year = {1972}, volume = {23}, pages = {435--441}, fjournal = {Archiv der Mathematik}, mrclass = {55F05}, mrnumber = {MR0321082 (47 \#9615)}, mrreviewer = {A. K. Bousfield} } % issn = {0003-889X}, @ARTICLE{strom:cofib-ii, author = {Str{\o}m, Arne}, title = {Note on cofibrations. {II}}, journal = {Math. Scand.}, year = {1968}, volume = {22}, pages = {130--142 (1969)}, fjournal = {Mathematica Scandinavica}, issn = {0025-5521}, mrclass = {55.50}, mrnumber = {MR0243525 (39 \#4846)}, mrreviewer = {J. Dugundji} } @ARTICLE{strom:cofib, author = {Str{\o}m, Arne}, title = {Note on cofibrations}, journal = {Math. Scand.}, year = {1966}, volume = {19}, pages = {11--14}, fjournal = {Mathematica Scandinavica}, issn = {0025-5521}, mrclass = {55.40 (54.00)}, mrnumber = {MR0211403 (35 \#2284)}, mrreviewer = {J. Dugundji} } @ARTICLE{MR0485246, author = {Szabo, Manfred E.}, title = {The logic of closed categories}, journal = {Notre Dame J. Formal Logic}, year = {1977}, volume = {18}, pages = {441--457}, number = {3}, fjournal = {Notre Dame Journal of Formal Logic}, issn = {0029-4527}, mrclass = {02D99 (02J99 18D15)}, mrnumber = {MR0485246 (58 \#5093)}, mrreviewer = {J. Lambek} } @UNPUBLISHED{tabuada:spectral-cats, author = {Goncalo Tabuada}, title = {Homotopy theory of Spectral categories}, note = {arXiv:0801.4524} } @ARTICLE{tabuada:modelcat-dgcat, author = {Tabuada, Goncalo}, title = {Une structure de cat\'egorie de mod\`eles de {Q}uillen sur la cat\'egorie des dg-cat\'egories}, journal = {C. R. Math. Acad. Sci. Paris}, year = {2005}, volume = {340}, pages = {15--19}, number = {1}, fjournal = {Comptes Rendus Math\'ematique. Acad\'emie des Sciences. Paris}, issn = {1631-073X}, mrclass = {18E99}, mrnumber = {MR2112034 (2005h:18033)} } @INCOLLECTION{MR723164, author = {Takeuti, Gaisi}, title = {Quantum set theory}, booktitle = {Current issues in quantum logic ({E}rice, 1979)}, publisher = {Plenum}, year = {1981}, volume = {8}, series = {Ettore Majorana Internat. Sci. Ser.: Phys. Sci.}, pages = {303--322}, address = {New York}, mrclass = {03G12 (03E70)}, mrnumber = {MR723164 (84j:03136)} } @ARTICLE{MR540672, author = {Takeuti, Gaisi}, title = {A transfer principle in harmonic analysis}, journal = {J. Symbolic Logic}, year = {1979}, volume = {44}, pages = {417--440}, number = {3}, coden = {JSYLA6}, fjournal = {The Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03E75 (03E40 03H20 22D05)}, mrnumber = {MR540672 (80h:03077)}, mrreviewer = {W. A. J. Luxemburg} } @INCOLLECTION{MR555569, author = {Takeuti, Gaisi}, title = {Boolean valued analysis}, booktitle = {Applications of sheaves ({P}roc. {R}es. {S}ympos. {A}ppl. {S}heaf {T}heory to {L}ogic, {A}lgebra and {A}nal., {U}niv. {D}urham, {D}urham, 1977)}, publisher = {Springer}, year = {1979}, volume = {753}, series = {Lecture Notes in Math.}, pages = {714--731}, address = {Berlin}, mrclass = {03E40 (47D25 81B05)}, mrnumber = {MR555569 (81c:03045)}, mrreviewer = {J. L. 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Lipshitz} } @INCOLLECTION{tt:heytval-ist, author = {Takeuti, Gaisi and Titani, Satoko}, title = {Heyting-valued universes of intuitionistic set theory}, booktitle = {Logic {S}ymposia, {H}akone 1979, 1980 ({H}akone, 1979/1980)}, publisher = {Springer}, year = {1981}, volume = {891}, series = {Lecture Notes in Math.}, pages = {189--306}, address = {Berlin}, mrclass = {03F55 (03E40)}, mrnumber = {MR656970 (84g:03100)}, mrreviewer = {Wim Veldman} } @BOOK{taylor:pracfdn, title = {Practical foundations of mathematics}, publisher = {Cambridge University Press}, year = {1999}, author = {Taylor, Paul}, volume = {59}, pages = {xii+572}, series = {Cambridge Studies in Advanced Mathematics}, address = {Cambridge}, isbn = {0-521-63107-6}, mrclass = {03-02 (00A30 03B15 03B40 03G30 18-02)}, mrnumber = {MR1694820 (2000h:03002)} } @ARTICLE{taylor:ordinals, author = {Taylor, Paul}, title = {Intuitionistic sets and ordinals}, journal = {J. Symbolic Logic}, year = {1996}, volume = {61}, pages = {705--744}, number = {3}, coden = {JSYLA6}, fjournal = {The Journal of Symbolic Logic}, issn = {0022-4812}, mrclass = {03E70 (03F55)}, mrnumber = {MR1412506 (97j:03102)}, mrreviewer = {Wim Ruitenburg} } @INPROCEEDINGS{MR0506548, author = {Tholen, Walter}, title = {Factorizations of cones along a functor}, booktitle = {Proceedings of the Second Symposium on Categorical Topology (Univ. Cape Town, Cape Town, 1976)}, year = {1977/78}, volume = {2}, number = {1-3}, pages = {335--353}, fjournal = {Quaestiones Mathematicae}, issn = {0379-9468}, journal = {Quaestiones Math.}, mrclass = {18A40}, mrnumber = {MR0506548 (58 \#22224)}, mrreviewer = {D. Pumplun} } @ARTICLE{tholen:ordtop, author = {Tholen, Walter}, title = {Ordered topological structures}, journal = {Topology Appl.}, year = {2009}, volume = {156}, pages = {2148--2157}, number = {12}, coden = {TIAPD9}, fjournal = {Topology and its Applications}, issn = {0166-8641}, mrclass = {18B30 (06B35 54A20)}, mrnumber = {MR2532144} } @INCOLLECTION{MR1854596, author = {Tholen, Walter}, title = {Essential weak factorization systems}, booktitle = {Contributions to general algebra, 13 (Velk\'e Karlovice, 1999/Dresden, 2000)}, publisher = {Heyn}, year = {2001}, pages = {321--333}, address = {Klagenfurt}, mrclass = {18A32 (18G05)}, mrnumber = {MR1854596 (2002f:18004)} } @ARTICLE{tholen:pro-multiadjt, author = {Tholen, Walter}, title = {Pro-categories and multiadjoint functors}, journal = {Canad. J. Math.}, year = {1984}, volume = {36}, pages = {144--155}, number = {1}, coden = {CJMAAB}, fjournal = {Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques}, issn = {0008-414X}, mrclass = {18A40}, mrnumber = {MR733712 (85j:18002)}, mrreviewer = {Timothy Porter} } @ARTICLE{tholen:total, author = {Tholen, Walter}, title = {Note on total categories}, journal = {Bull. Austral. Math. Soc.}, year = {1980}, volume = {21}, pages = {169--173}, number = {2}, coden = {ALNBAB}, fjournal = {Bulletin of the Australian Mathematical Society}, issn = {0004-9727}, mrclass = {18A40 (18B30)}, mrnumber = {MR574836 (81h:18002)}, mrreviewer = {Ji{\v{r}}{\'{\i}} Ad{\'a}mek} } @INCOLLECTION{t:lifting-semifinal, author = {Tholen, Walter}, title = {Lifting semifinal liftings}, booktitle = {Categorical topology (Proc. Internat. Conf., Free Univ. Berlin, Berlin, 1978)}, publisher = {Springer}, year = {1979}, volume = {719}, series = {Lecture Notes in Math.}, pages = {376--385}, address = {Berlin}, mrclass = {18A40 (18A99)}, mrnumber = {MR544661 (81a:18004)}, mrreviewer = {A. Pultr} } @ARTICLE{tholen:semitop-i, author = {Tholen, Walter}, title = {Semitopological functors. {I}}, journal = {J. Pure Appl. Algebra}, year = {1979}, volume = {15}, pages = {53--73}, number = {1}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D99 (18A40 54B30)}, mrnumber = {MR532963 (80k:18012a)}, mrreviewer = {M. Hu{\v{s}}ek} } @ARTICLE{tw:semitop-ii, author = {Tholen, Walter and Wischnewsky, Manfred B.}, title = {Semitopological functors. {II}. {E}xternal characterizations}, journal = {J. Pure Appl. Algebra}, year = {1979}, volume = {15}, pages = {75--92}, number = {1}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18D99 (18A40 54B30)}, mrnumber = {MR532964 (80k:18012b)}, mrreviewer = {M. Hu{\v{s}}ek} } @ARTICLE{thomason:cat-model, author = {Thomason, R. W.}, title = {Cat as a closed model category}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = {1980}, volume = {21}, pages = {305--324}, number = {3}, coden = {CTGDBR}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle}, issn = {0008-0004}, mrclass = {18A99 (55U35)}, mrnumber = {MR591388 (82b:18005)}, mrreviewer = {Harold Hastings} } @ARTICLE{thomason:uniq-deloop, author = {Thomason, R. W.}, title = {Uniqueness of delooping machines}, journal = {Duke Math. J.}, year = {1979}, volume = {46}, pages = {217--252}, number = {2}, coden = {DUMJAO}, fjournal = {Duke Mathematical Journal}, issn = {0012-7094}, mrclass = {55P35 (55R35)}, mrnumber = {MR534053 (80e:55013)}, mrreviewer = {J. F. Adams} } @BOOK{thron:top-str, title = {Topological structures}, publisher = {Holt}, year = {1966}, author = {Thron, Wolfgang J.}, pages = {x+240}, address = {Rinehart and Winston, New York}, mrclass = {54.00}, mrnumber = {MR0200892 (34 \#778)}, mrreviewer = {J. Dugundji} } @ARTICLE{toen:locconst, author = {Toen, Bertrand}, title = {Vers une interpr\'etation galoisienne de la th\'eorie de l'homotopie}, journal = {Cah. Topol. G\'eom. Diff\'er. Cat\'eg.}, year = {2002}, volume = {43}, pages = {257--312}, number = {4}, eprint = {arXiv:math.AT/0007157}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques}, issn = {1245-530X}, mrclass = {55U40 (18G30 55P35)}, mrnumber = {MR1949660 (2003m:55030)} } @ARTICLE{toen:ax, author = {To{\"e}n, Bertrand}, title = {Vers une axiomatisation de la th\'eorie des cat\'egories sup\'erieures}, journal = {$K$-Theory}, year = {2005}, volume = {34}, pages = {233--263}, number = {3}, coden = {KTHEEO}, eprint = {math.CT/0409598}, fjournal = {$K$-Theory. An Interdisciplinary Journal for the Development, Application, and Influence of $K$-Theory in the Mathematical Sciences}, issn = {0920-3036}, mrclass = {55U35 (18D05 18G55)}, mrnumber = {MR2182378 (2006m:55041)}, mrreviewer = {Mamuka Jibladze} } @ARTICLE{trnkova:cls-setfrs-i, author = {Trnkov{\'a}, V{\v{e}}ra}, title = {On descriptive classification of set-functors. {I}}, journal = {Comment. Math. Univ. Carolinae}, year = {1971}, volume = {12}, pages = {143--174}, fjournal = {Commentationes Mathematicae Universitatis Carolinae}, issn = {0010-2628}, mrclass = {18A99 (04A15)}, mrnumber = {MR0294445 (45 \#3515)}, mrreviewer = {O. Wyler} } @ARTICLE{trnkova:cls-setfrs-ii, author = {Trnkov{\'a}, V{\v{e}}ra}, title = {On descriptive classification of set-functors. {II}}, journal = {Comment. Math. Univ. Carolinae}, year = {1971}, volume = {12}, pages = {345--357}, fjournal = {Commentationes Mathematicae Universitatis Carolinae}, issn = {0010-2628}, mrclass = {18A99 (04A15)}, mrnumber = {MR0294446 (45 \#3516)}, mrreviewer = {O. Wyler} } @BOOK{tvd:constructivism-i, title = {Constructivism in mathematics. {V}ol. {I}}, publisher = {North-Holland Publishing Co.}, year = {1988}, author = {Troelstra, A. S. and van Dalen, D.}, volume = {121}, pages = {xx+342+XIV}, series = {Studies in Logic and the Foundations of Mathematics}, address = {Amsterdam}, isbn = {0-444-70266-0; 0-444-70506-6}, mrclass = {03-01 (03D20 03Fxx)}, mrnumber = {MR966421 (90e:03002a)}, mrreviewer = {G. E. Mints} } @BOOK{tvd:constructivism-ii, title = {Constructivism in mathematics. {V}ol. {II}}, publisher = {North-Holland Publishing Co.}, year = {1988}, author = {Troelstra, A. S. and van Dalen, D.}, volume = {123}, pages = {i--xviii and 345--880 and I--LII}, series = {Studies in Logic and the Foundations of Mathematics}, address = {Amsterdam}, note = {An introduction}, isbn = {0-444-70358-6}, mrclass = {03-01 (03B15 03Fxx 03G30)}, mrnumber = {MR970277 (90e:03002b)}, mrreviewer = {G. E. Mints} } @ARTICLE{ulmer:dense-rel-adjt, author = {Ulmer, Friedrich}, title = {Properties of dense and relative adjoint functors}, journal = {J. Algebra}, year = {1968}, volume = {8}, pages = {77--95}, fjournal = {Journal of Algebra}, issn = {0021-8693}, mrclass = {18.10}, mrnumber = {MR0222138 (36 \#5190)}, mrreviewer = {M. Barr} } @ARTICLE{exact-yoneda, author = {Van den Bril, Luc}, title = {Exactitude dans les {Y}oneda-structures}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = {1982}, volume = {23}, pages = {215--224}, number = {2}, coden = {CTGDBR}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle}, issn = {0008-0004}, mrclass = {18C99 (18D05)}, mrnumber = {MR667400 (84a:18012)}, mrreviewer = {G. M. Kelly} } @PHDTHESIS{verity:base-change, author = {Dominic Verity}, title = {Enriched categories, internal categories, and change of base}, school = {University of Cambridge}, year = {1992}, month = {April}, note = {Macquarie Mathematics Report No. 93-123} } @INCOLLECTION{vickers:loctopsp, author = {Vickers, Steven}, title = {Locales and toposes as spaces}, booktitle = {Handbook of spatial logics}, publisher = {Springer}, year = {2007}, pages = {429--496}, address = {Dordrecht}, note = {Preprint available online at \url{http://www.cs.bham.ac.uk/~sjv/papersfull.php\#LocTopSpaces}}, mrclass = {03G30 (18B25 54B30)}, mrnumber = {MR2393892} } @ARTICLE{MR2182680, author = {Vickers, Steven}, title = {Localic completion of generalized metric spaces. {I}}, journal = {Theory Appl. Categ.}, year = {2005}, volume = {14}, pages = {No. 15, 328--356 (electronic)}, fjournal = {Theory and Applications of Categories}, issn = {1201-561X}, mrclass = {54E50 (03G30 06D22 18D20 26E40)}, mrnumber = {MR2182680 (2006h:54025)}, mrreviewer = {Hans-Peter A. K{\"u}nzi} } @ARTICLE{MR1996461, author = {Vogt, R. M.}, title = {Cofibrant operads and universal {$E\sb \infty$} operads}, journal = {Topology Appl.}, year = {2003}, volume = {133}, pages = {69--87}, number = {1}, coden = {TIAPD9}, fjournal = {Topology and its Applications}, issn = {0166-8641}, mrclass = {18D50 (55P48)}, mrnumber = {MR1996461 (2004e:18014)} } @ARTICLE{walters:sheaves-cauchy-2, author = {Walters, R.F.C.}, title = {Sheaves on sites as {C}auchy-complete categories}, journal = {J. Pure Appl. Algebra}, year = {1982}, volume = {24}, pages = {95--102}, number = {1}, coden = {JPAAA}, fjournal = {Journal of Pure and Applied Algebra}, issn = {0022-4049}, mrclass = {18F20 (18F10)}, mrnumber = {MR647583 (83e:18006)}, mrreviewer = {Harvey Wolff} } @ARTICLE{walters:sheaves-cauchy-1, author = {Walters, R.F.C.}, title = {Sheaves and {C}auchy-complete categories}, journal = {Cahiers Topologie G\'eom. Diff\'erentielle}, year = 1981, volume = 22, pages = {283--286}, number = 3, note = {Third Colloquium on Categories, Part IV (Amiens, 1980)}, coden = {CTGDBR}, fjournal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle}, issn = {0008-0004}, mrclass = {18F20 (03G30 18D20)}, mrnumber = {MR649076 (83f:18011)}, mrreviewer = {R. H. Street} } @ARTICLE{wang:truth-def, author = {Wang, Hao}, title = {Truth definitions and consistency proofs}, journal = {Trans. Amer. Math. Soc.}, year = {1952}, volume = {73}, pages = {243--275}, fjournal = {Transactions of the American Mathematical Society}, issn = {0002-9947}, mrclass = {02.0X}, mrnumber = {MR0049136 (14,123a)}, mrreviewer = {G. Kreisel} } @ARTICLE{MR0396578, author = {Waterhouse, William C.}, title = {Basically bounded functors and flat sheaves}, journal = {Pacific J. Math.}, year = {1975}, volume = {57}, pages = {597--610}, number = {2}, fjournal = {Pacific Journal of Mathematics}, issn = {0030-8730}, mrclass = {14F20}, mrnumber = {MR0396578 (53 \#441)}, mrreviewer = {Andy R. Magid} } @ARTICLE{weaver:axiomatizing, author = {Nik Weaver}, title = {Axiomatizing mathematical conceptualism in third order arithmetic}, year = {2009}, month = may, abstract = {We review the philosophical framework of mathematical conceptualism as an alternative to set-theoretic foundations and show how mainstream mathematics can be developed on this basis. The paper includes an explicit axiomatization of the basic principles of conceptualism in a formal system CM set in the language of third order arithmetic.}, comments = {31 pages}, eprint = {0905.1675}, file = {Axiomatizing mathematical conceptualism in third order arithmetic 0905.1675v1.pdf:Weaver, Nik/Axiomatizing mathematical conceptualism in third order arithmetic 0905.1675v1.pdf:PDF}, oai2identifier = {0905.1675} } @ARTICLE{weaver:concept, author = {Nik Weaver}, title = {The concept of a set}, year = {2009}, month = may, abstract = {Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three different kinds of logic (classical, intuitionistic, and minimal). A foundational system incorporating this analysis and based on the principles of mathematical conceptualism accords better with actual mathematical practice than Zermelo-Fraenkel set theory does.}, comments = {11 pages}, eprint = {0905.1677}, file = {The concept of a set 0905.1677v1.pdf:Weaver, Nik/The concept of a set 0905.1677v1.pdf:PDF}, oai2identifier = {0905.1677} } @ARTICLE{weaver:constructive, author = {Nik Weaver}, title = {Constructive truth and circularity}, year = {2009}, month = may, abstract = {We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.}, comments = {10 pages}, eprint = {0905.1681}, file = {Constructive truth and circularity 0905.1681v1.pdf:Weaver, Nik/Constructive truth and circularity 0905.1681v1.pdf:PDF}, oai2identifier = {0905.1681} } @ARTICLE{weaver:is, author = {Nik Weaver}, title = {Is set theory indispensable?}, year = {2009}, month = may, abstract = {Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much weaker systems which are essentially number-theoretic in nature. Feferman has observed that this severely undercuts a famous argument of Quine and Putnam according to which set theoretic platonism is validated by the fact that mathematics is "indispensable" for some successful scientific theories (since in fact ZFC is not needed for the mathematics that is currently used in science). I extend this critique in three ways: (1) not only is it possible to formalize core mathematics in these weaker systems, they are in important ways better suited to the task than ZFC; (2) an improved analysis of the proof-theoretic strength of predicative theories shows that most if not all of the already rare examples of mainstream theorems whose proofs are currently thought to require metaphysically substantial set-theoretic principles actually do not; and (3) set theory itself, as it is actually practiced, is best understood in formalist, not platonic, terms, so that in a real sense *set theory is not even indispensable for set theory*. I also make the point that even if ZFC is consistent, there are good reasons to suspect that some number-theoretic assertions provable in ZFC may be false. This suggests that set theory should not be considered central to mathematics.}, comments = {21 pages}, eprint = {0905.1680}, file = {Is set theory indispensable 0905.1680v1.pdf:Weaver, Nik/Is set theory indispensable 0905.1680v1.pdf:PDF}, oai2identifier = {0905.1680} } @ARTICLE{weaver:mathematical, author = {Nik Weaver}, title = {Mathematical conceptualism}, year = {2007}, abstract = {This is an explanation and defense of "mathematical conceptualism" for a general mathematical and philosophical audience. I make a case that it is cogent, rigorous, attractive, and better suited to ordinary mathematical practice than all other foundational stances.}, comments = {18 pages}, eprint = {math/0509246}, file = {Mathematical conceptualism 0509246.pdf:Weaver, Nik/Mathematical conceptualism 0509246.pdf:PDF}, oai2identifier = {math/0509246} } @ARTICLE{weber:2toposes, author = {Weber, Mark}, title = {Yoneda structures from 2-toposes}, journal = {Appl. Categ. Structures}, year = {2007}, volume = {15}, pages = {259--323}, number = {3}, coden = {ACASE6}, fjournal = {Applied Categorical Structures. A Journal Devoted to Applications of Categorical Methods in Algebra, Analysis, Order, Topology and Computer Science}, issn = {0927-2852}, mrclass = {18A05 (18A15 18B25 18D05)}, mrnumber = {MR2320763} } @ARTICLE{weber:fam-pra, author = {Weber, Mark}, title = {Familial 2-functors and parametric right adjoints}, journal = {Theory Appl. 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K. Bousfield}, } @article {b:fgfheyting, AUTHOR = {Bellissima, Fabio}, TITLE = {Finitely generated free {H}eyting algebras}, JOURNAL = {J. Symbolic Logic}, FJOURNAL = {The Journal of Symbolic Logic}, VOLUME = {51}, YEAR = {1986}, NUMBER = {1}, PAGES = {152--165}, CODEN = {JSYLA6}, MRCLASS = {03G25 (03B55 03F55 06D20 08B20)}, MRNUMBER = {830082 (87k:03081)}, MRREVIEWER = {R. Sh. Grigolia} } % ISSN = {0022-4812}, % DOI = {10.2307/2273952}, % URL = {http://dx.doi.org/10.2307/2273952}, @article {bg:fgfhbirkhoff, AUTHOR = {Bezhanishvili, Nick and Gehrke, Mai}, TITLE = {Finitely generated free {H}eyting algebras via {B}irkhoff duality and coalgebra}, JOURNAL = {Log. Methods Comput. Sci.}, FJOURNAL = {Logical Methods in Computer Science}, VOLUME = {7}, YEAR = {2011}, NUMBER = {2}, PAGES = {2:9, 24}, ISSN = {1860-5974}, MRCLASS = {03G20 (06D50)}, MRNUMBER = {2802818}, MRREVIEWER = {R. Sh. 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Slides available at \texttt{http://www-lmpa.univ-littoral.fr/CT08/slides/Lack.pdf}}, month = {June}, year = 2008 } @article{ls:limlax, title = "Enhanced 2-categories and limits for lax morphisms", journal = "Advances in Mathematics", volume = "229", number = "1", pages = "294--356", year = "2012", note = "arXiv:1104.2111", issn = "0001-8708", doi = "10.1016/j.aim.2011.08.014", url = "http://www.sciencedirect.com/science/article/pii/S000187081100315X", author = "Stephen Lack and Michael Shulman", } @Unpublished{shulman:ccrtraces, author = {Michael Shulman}, title = {Traces in monoidal categories and bicategories}, note = {Talk at CCR La Jolla. Slides available at \texttt{http://www.math.uchicago.edu/$\sim$shulman/research/ccrtraces.pdf}}, month = {August}, year = 2008 } @Unpublished{shulman:mat-struct, author = {Michael Shulman}, title = {Comparing material and structural set theories}, note = {In preparation}, year = {2017} } @Unpublished{shulman:stacksem, author = {Michael Shulman}, title = {Stack semantics and unbounded quantifiers in topos theory}, note = {In preparation}, year = 2017 } @Unpublished{shulman:etlc, author = {Michael Shulman}, title = {The elementary theory of large categories}, note = {In preparation}, year = {2010} } @Unpublished{rs:2sheaves, author = {David Rydh and Michael Shulman}, title = {Regularity and exactness for 2-sheaves}, note = {In preparation. Some work in progress available at \url{http://www.ncatlab.org/michaelshulman/show/2-categorical+logic}}} @Unpublished{shulman:2logic, author = {Michael Shulman}, title = {The internal logic of a 2-topos}, note = {In preparation. Work in progress available at\\ \url{http://www.ncatlab.org/michaelshulman/show/2-categorical+logic}}, year = {2010}} @Unpublished{shulman:2cofc, author = {Michael Shulman}, title = {2-categories of classes}, note = {In preparation}, year = {2010}} @Article{cs:multicats, author = {G.S.H. Cruttwell and Michael Shulman}, title = {A unified framework for generalized multicategories}, journal = {Theory Appl. Categ.}, year = 2010, volume = 24, pages = {580--655}, note = {arXiv:0907.2460}} @Unpublished{shulman:vequip, author = {Michael Shulman}, title = {Limits and completions in formal category theory}, note = {In preparation} } @Unpublished{shulman:cosmoi, author = {Michael Shulman}, title = {Categories enriched in monoidal fibrations}, note = {In preparation} } @Unpublished{shulman:extrmultitalk, author = {Michael Shulman}, title = {Extraordinary multicategories}, note = {Talk at CMS Summer Meeting; slides available at \url{http://www.math.ucsd.edu/~mshulman/papers/cms2010talk.pdf}}, year = 2010} @Unpublished{shulman:extrmultiblog, author = {Michael Shulman}, title = {Extraordinary 2-multicategories}, note = {Blog post available at \url{http://golem.ph.utexas.edu/category/2010/03/extraordinary_2multicategories.html}}, year = 2010} @Article{shulman:psalg, author = {Michael Shulman}, title = {Not every pseudoalgebra is equivalent to a strict one}, journal = {Adv. Math.}, year = 2012, volume = 229, number = 3, pages = {2024--2041}, note = {arXiv:1005.1520}} @Misc{nlab:ptder, author = {Michael Shulman and others}, title = {pointed derivator}, note = {\url{http://nlab.mathforge.org/nlab/show/pointed+derivator}}} @Misc{shulman:pi1s1-blog, author = {Michael Shulman}, title = {A formal proof that $\pi_1(S^1)=\mathbb{Z}$}, howpublished = {\url{http://homotopytypetheory.org/2011/04/29/a-formal-proof-that-pi1s1-is-z/}}, year = 2011} @Misc{shulman:univsubtop, author = {Michael Shulman}, title = {Modeling univalence in subtoposes}, howpublished = {\url{http://homotopytypetheory.org/2011/12/06/modeling-univalence-in-subtoposes/}}, month = {Dec}, year = 2011} @Unpublished{ls:hits, author = {Peter LeFanu Lumsdaine and Michael Shulman}, title = {Semantics of higher inductive types}, note = {arXiv:1705.07088}, year = 2017} @Article{shulman:elreedy, author = {Michael Shulman}, title = {The univalence axiom for elegant {Reedy} presheaves}, journal = {Homology, Homotopy, and Applications}, year = 2015, volume = 17, number = 2, pages = {81--106}, note = {arXiv:1307.6248}} @Article{shulman:exsite, author = {Michael Shulman}, title = {Exact completions and small sheaves}, journal = {Theory and Applications of Categories}, year = 2012, volume = 27, number = 7, note = {arXiv:1203.4318}, pages = {97--173}} @Unpublished{shulman:smbicat, author = {Michael Shulman}, title = {Constructing symmetric monoidal bicategories}, year = {2010}, note = {arXiv:1004.0993}} @Article{gs:freecocomp, author = {Richard Garner and Michael Shulman}, title = {Enriched categories as a free cocompletion}, journal = {Adv. Math}, volume = {289}, note = {arXiv:1301.3191}, year = 2016, pages = {1--94}} @article {blass:no-ultrafilters, AUTHOR = {Blass, Andreas}, TITLE = {A model without ultrafilters}, JOURNAL = {Bull. Acad. Polon. Sci. S\'er. Sci. Math. Astronom. Phys.}, FJOURNAL = {Bulletin de l'Acad\'emie Polonaise des Sciences. S\'erie des Sciences Math\'ematiques, Astronomiques et Physiques}, VOLUME = {25}, YEAR = {1977}, NUMBER = {4}, PAGES = {329--331}, ISSN = {0001-4117}, MRCLASS = {02K05}, MRNUMBER = {0476510 (57 \#16070)}, MRREVIEWER = {James H. Schmerl}, } @incollection {hofmann:ssdts, AUTHOR = {Hofmann, Martin}, TITLE = {Syntax and semantics of dependent types}, BOOKTITLE = {Semantics and logics of computation ({C}ambridge, 1995)}, SERIES = {Publ. Newton Inst.}, VOLUME = {14}, PAGES = {79--130}, PUBLISHER = {Cambridge Univ. 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Categ.}, year = 2013, volume = 28, number = 8, pages = {213--240}} @article{bw:ends, title = "The calculus of ends over a base topos", journal = "Journal of Pure and Applied Algebra", volume = "56", number = "3", pages = "211 - 220", year = "1989", note = "", issn = "0022-4049", doi = "10.1016/0022-4049(89)90057-1", url = "http://www.sciencedirect.com/science/article/pii/0022404989900571", author = "R. Betti and R.F.C. Walters" } @Article{br:descent, author = {Jean B\'enabou and Jacques Robaud}, title = {Monades et descente}, journal = {C. R. Acad. Sc. Paris, Serie A}, year = 1970, pages = {96--98}, month = {January}} @article{dt:exppppc, title = "Exponentiable morphisms, partial products and pullback complements", journal = "Journal of Pure and Applied Algebra", volume = "49", number = "1–2", pages = "103 - 116", year = "1987", note = "", issn = "0022-4049", doi = "10.1016/0022-4049(87)90124-1", url = "http://www.sciencedirect.com/science/article/pii/0022404987901241", author = "Roy Dyckhoff and Walter Tholen" } @Article{kl:essloc, author = {G. M. Kelly and F. W. 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Pure Appl. Logic}, FJOURNAL = {Annals of Pure and Applied Logic}, VOLUME = {164}, eprint = {arXiv:1205.5527}, YEAR = {2013}, NUMBER = {10}, PAGES = {957--988}, CODEN = {APALD7}, MRCLASS = {03B15 (03G30 18D30)}, MRNUMBER = {3069019} } % ISSN = {0168-0072}, % DOI = {10.1016/j.apal.2013.05.002}, % URL = {http://dx.doi.org/10.1016/j.apal.2013.05.002}, @INPROCEEDINGS{wadler:free-theorems, author = {Philip Wadler}, title = {Theorems for free!}, booktitle = {Functional Programming Languages and Computer Architecture}, year = {1989}, pages = {347--359}, publisher = {ACM Press} } @Unpublished{klv:ssetmodel, author = {Chris Kapulkin and Peter LeFanu Lumsdaine}, title = {The Simplicial Model of Univalent Foundations (after {Voevodsky})}, note = {arXiv:1211.2851}, year = 2012} @inproceedings{lh:canonicity, author = {Licata, Daniel R. and Harper, Robert}, title = {Canonicity for 2-dimensional type theory}, booktitle = {Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages}, series = {POPL '12}, year = {2012}, location = {Philadelphia, PA, USA}, pages = {337--348}, numpages = {12}, publisher = {ACM}, address = {New York, NY, USA}, keywords = {category theory, dependent types, homotopy type theory, type theory}, } % isbn = {978-1-4503-1083-3}, % url = {http://doi.acm.org/10.1145/2103656.2103697}, % doi = {10.1145/2103656.2103697}, % acmid = {2103697}, @inproceedings{huet:hou30yrs, author = {Huet, G{\'e}rard P.}, title = {Higher Order Unification 30 Years Later}, booktitle = {Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics}, series = {TPHOLs '02}, year = {2002}, isbn = {3-540-44039-9}, pages = {3--12}, numpages = {10}, url = {http://dl.acm.org/citation.cfm?id=646529.695200}, acmid = {695200}, publisher = {Springer-Verlag}, address = {London, UK, UK}, } @Article{johnson:modreedy, author = {Mark W. 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Categ}, year = {2003}, volume = {14}, pages = {1--45} } @INPROCEEDINGS{ms:sconing, author = {John C. Mitchell and Andre Scedrov}, title = {Notes on Sconing and Relators}, booktitle = {}, year = {1993}, pages = {352--378}, publisher = {Springer} } @incollection{ag:colldtt, Author = {Aczel, Peter and Gambino, Nicola}, Booktitle = {Types for proofs and programs}, Pages = {1--23}, Publisher = {Springer}, Title = {Collection principles in dependent type theory}, Year = {2002}} @Unpublished{bourke:2dmonadicity, author = {John Bourke}, title = {Two dimensional monadicity}, note = {arXiv:1212.5123}, year = {2012}} @article{jj:ccat-exptop, title={Continuous categories and exponentiable toposes}, author={Johnstone, Peter and Joyal, Andr{\'e}}, journal={Journal of Pure and Applied Algebra}, volume={25}, number={3}, pages={255--296}, year={1982}, publisher={North-Holland} } @article {rezk:cor-cpncats, AUTHOR = {Rezk, Charles}, TITLE = {Correction to ``{A} {C}artesian presentation of weak {$n$}-categories'' [MR2578310]}, JOURNAL = {Geom. Topol.}, FJOURNAL = {Geometry \& Topology}, VOLUME = {14}, YEAR = {2010}, NUMBER = {4}, PAGES = {2301--2304}, ISSN = {1465-3060}, MRCLASS = {18D05 (55U40)}, MRNUMBER = {2740648 (2011j:18008)}, DOI = {10.2140/gt.2010.14.2301}, URL = {http://dx.doi.org/10.2140/gt.2010.14.2301}, } @article {rezk:cpncats, AUTHOR = {Rezk, Charles}, TITLE = {A {C}artesian presentation of weak {$n$}-categories}, JOURNAL = {Geom. Topol.}, FJOURNAL = {Geometry \& Topology}, VOLUME = {14}, YEAR = {2010}, NUMBER = {1}, PAGES = {521--571}, ISSN = {1465-3060}, MRCLASS = {18D05 (55U40)}, MRNUMBER = {2578310 (2010m:18005)}, DOI = {10.2140/gt.2010.14.521}, URL = {http://dx.doi.org/10.2140/gt.2010.14.521}, } @Book{hottbook, author = {{Univalent Foundations Program}}, title = {Homotopy Type Theory: Univalent Foundations of Mathematics}, shortauthor = {UFP}, publisher = {\url{http://homotopytypetheory.org/book/}}, edition = {first}, year = 2013} @InProceedings{ss:qgftchtt, author = {Urs Schreiber and Michael Shulman}, title = {Quantum gauge field theory in cohesive homotopy type theory}, booktitle = {QPL'12}, year = 2012, note = {\url{http://ncatlab.org/schreiber/files/QFTinCohesiveHoTT.pdf}}} @book{bishop:fca, title={Foundations of constructive analysis}, author={Bishop, E.}, series={McGraw-Hill series in higher mathematics}, year={1967}, publisher={McGraw-Hill} } @Book{bb:constr-analysis, author = {Errett Bishop and Douglas Bridges}, title = {Constructive analysis}, publisher = {Springer--Verlag}, year = 1985} @Article{shulman:eicats, author = {Michael Shulman}, title = {Enriched indexed categories}, journal = {Theory and Applications of Categories}, year = 2013, volume = 28, number = 21, pages = {616-695}} @Unpublished{gps:mv, author = {Moritz Groth and Kate Ponto and Michael Shulman}, title = {Mayer-Vietoris sequences in stable derivators}, note = {Submitted. arXiv:1306.2072}} @Unpublished{gps:additivity, author = {Moritz Groth and Kate Ponto and Michael Shulman}, title = {The additivity of traces in monoidal derivators}, note = {Submitted. arXiv:1212.3277}} @Article{pare:sclim, author = {Robert Par\'e}, title = {Simply connected limits}, journal = {Canad. J. Math.}, year = 1990, volume = 42, pages = {731--746}} @Unpublished{cisinski:elegant, author = {Denis-Charles Cisinski}, title = {Univalent universes for elegant models of homotopy types}, note = {arXiv:1406.0058}, year = 2014} @Unpublished{awodey:natmodels, author = {Steve Awodey}, title = {Natural models of homotopy type theory}, note = {arXiv:1406.3219}, year = 2014} @Article{rv:reedy, author = {Emily Riehl and Dominic Verity}, title = {The theory and practice of {Reedy} categories}, journal = {Theory and Applications of Categories}, year = 2014, volume = 29, number = 9, pages = {256--301}, note = {\url{http://www.tac.mta.ca/tac/volumes/29/9/29-09abs.html}}} @Article{boolos:cut, author = {George Boolos}, title = {Don't eliminate cut}, journal = {Journal of Philosophical Logic}, year = 1984, volume = 13, number = 4, pages = {373--378}} @article {seely:lccc-tt, AUTHOR = {Seely, R. A. G.}, TITLE = {Locally {C}artesian closed categories and type theory}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {95}, YEAR = {1984}, NUMBER = {1}, PAGES = {33--48}, ISSN = {0305-0041}, CODEN = {MPCPCO}, MRCLASS = {18D15 (03B15 03F55 03G30)}, MRNUMBER = {727078 (86b:18008)}, MRREVIEWER = {S. B. Niefield}, DOI = {10.1017/S0305004100061284}, URL = {http://dx.doi.org/10.1017/S0305004100061284}, } @article {cp:local-selfmaps, AUTHOR = {Casacuberta, Carles and Peschke, Georg}, TITLE = {Localizing with respect to self-maps of the circle}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {339}, YEAR = {1993}, NUMBER = {1}, PAGES = {117--140}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {55P60 (18G99 20J05 55N25 55P10)}, MRNUMBER = {1123451 (93k:55012)}, MRREVIEWER = {Richard John Steiner}, DOI = {10.2307/2154211}, URL = {http://dx.doi.org/10.2307/2154211}, } @Unpublished{cg:iticons, author = {Eugenia Cheng and Nick Gurski}, title = {Iterated icons}, note = {arXiv:1308.6495}, year = 2013} @Unpublished{bch:tt-cubical, author = {Marc Bezem and Thierry Coquand and Simon Huber}, title = {A model of type theory in cubical sets}, note = {\url{http://www.cse.chalmers.se/~coquand/mod1.pdf}}, month = {March}, year = 2014} @article {elmendorf:theorem, AUTHOR = {Elmendorf, A. D.}, TITLE = {Systems of fixed point sets}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, VOLUME = {277}, YEAR = {1983}, NUMBER = {1}, PAGES = {275--284}, ISSN = {0002-9947}, CODEN = {TAMTAM}, MRCLASS = {57S99 (55N25)}, MRNUMBER = {690052 (84f:57029)}, MRREVIEWER = {J. P. May}, DOI = {10.2307/1999356}, URL = {http://dx.doi.org/10.2307/1999356}, } @Book{riehl:cht, author = {Emily Riehl}, title = {Categorical homotopy theory}, publisher = {Cambridge University Press}, year = 2014, volume = 24, series = {New mathematical monographs}} @article {angeltveit:enr-reedy, AUTHOR = {Angeltveit, Vigleik}, TITLE = {Enriched {Reedy} categories}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, note = {Corrected version available at arXiv:math/0612137v2.}, VOLUME = {136}, YEAR = {2008}, NUMBER = {7}, PAGES = {2323--2332}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {18G55}, MRNUMBER = {2390498 (2009a:18009)}, MRREVIEWER = {Birgit Richter}, DOI = {10.1090/S0002-9939-08-09185-5}, URL = {http://dx.doi.org/10.1090/S0002-9939-08-09185-5}, } @Unpublished{shulman:eiuniv, author = {Michael Shulman}, title = {The univalence axiom for {EI} diagrams}, note = {To appear in HHA. arXiv:1508.02410}, year = 2017} @article {gambino:wgtlim, AUTHOR = {Gambino, Nicola}, TITLE = {Weighted limits in simplicial homotopy theory}, JOURNAL = {J. Pure Appl. Algebra}, FJOURNAL = {Journal of Pure and Applied Algebra}, VOLUME = {214}, YEAR = {2010}, NUMBER = {7}, PAGES = {1193--1199}, ISSN = {0022-4049}, CODEN = {JPAAA2}, MRCLASS = {18G55 (18D20 18G30 55U35)}, MRNUMBER = {2586997 (2011e:18030)}, MRREVIEWER = {J{\'e}r{\^o}me Scherer}, DOI = {10.1016/j.jpaa.2009.10.006}, URL = {http://dx.doi.org/10.1016/j.jpaa.2009.10.006}, } @incollection {pare:abscoeq, AUTHOR = {Par{\'e}, Robert}, TITLE = {Absolute coequalizers}, BOOKTITLE = {Category {T}heory, {H}omology {T}heory and their {A}pplications, {I} ({B}attelle {I}nstitute {C}onference, {S}eattle, {W}ash., 1968, {V}ol. {O}ne)}, PAGES = {132--145}, PUBLISHER = {Springer, Berlin}, YEAR = {1969}, MRCLASS = {18.10}, MRNUMBER = {0244343 (39 \#5658)}, MRREVIEWER = {G. S. 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