## The collected works of F. W. Lawvere

Please inform us of any inaccuracies or missing works.

| Title |Source| Year |
|:------|:-----|:----:|
|[The Language of Algebra: Supplement](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1961-language-of-algebra-supplement.pdf)|TEMAC programmed learning materials|1961|
|[The Category of Probabilistic Mappings – With Applications to Stochastic Processes, Statistics, and Pattern Recognition](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1962-the-category-of-probabilistic-mappings.pdf)|Unpublished; seminar handout notes|1962|
|Functorial Semantics of Algebraic Theories|Original unpublished; Ph.D. thesis, Columbia University, 1963. See extended TAC reprint 2004|1963|
|[Functorial Semantics of Algebraic Theories (short notice)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1963-functorial-semantics-of-algebraic-theories-(short).pdf)|Proceedings of the National Academy of Science 50, No. 5 (November 1963), 869-872|1963|
|Functorial Automata Theory ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1963-functorial-automata-theory-abstract.pdf))|AMS Notices 603-151, vol 10 (1963), 477-478|1963|
|The group ring of a small category ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1963-the-group-ring-of-a-small-category-abstract.pdf))|Notices Amer. Math. Soc., 10, 280 (1963); Errata, Notices Amer. Math. Soc., 10, 516|1963|
|[An Elementary Theory of the Category of Sets (cf. 2005 long version with commentary)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1964-an-elementary-theory-of-the-category-of-sets.pdf)|Proceedings of the National Academy of Science 52, No. 6 (December 1964), 1506-1511|1964|
|[Algebraic Theories, Algebraic Categories, and Algebraic Functors](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1965-algebraic-theories-algebraic-categories-and-algebraic-functors.pdf)|Theory of Models; North-Holland, Amsterdam (1965), 413-418|1965|
|Functorial Semantics of Elementary Theories ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1965-functorial-semantics-of-elementary-theories-abstract.pdf))|J. Symb. Logic, 31, 294-295, 1966|1966|
|[The Category of Categories as a Foundation for Mathematics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1966-category-of-categories-as-a-foundation-for-mathematics.pdf)|La Jolla Conference on Categorical Algebra, Springer-Verlag (1966), 1-20|1966|
|[Presentations of right complete categories (abstract, followed Anders Kock's notes)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1966-presentations-of-right-complete-categories.pdf)|Oberwolfach meeting on category theory|1966|
|Theories as Categories and the Completeness Theorem ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1966-theories-as-categories-and-the-completeness-theorem-abstract.pdf))|Journal of Symbolic Logic, 32:562|1967|
|[Some Algebraic Problems in the Context of Functorial Semantic of Algebraic Theories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1968-some-algebraic-problems-in-the-context-of-functorial-semantic-of-algebraic-theories.pdf)|Springer Lecture Notes in Mathematics No. 61 (Reports of the Midwest Category Seminar II), Springer-Verlag (1968), 41-61|1968|
|[Ordinal Sums and Equational Doctrines](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1969-ordinal-sums-and-equational-doctrines.pdf)|Springer Lecture Notes in Mathematics No. 80, Springer-Verlag, 141-155.|1969|
|[Diagonal Arguments and Cartesian Closed Categories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1969-diagonal-arguments-and-cartesian-closed-categories.pdf)|Springer Lecture Notes in Mathematics No. 92, Springer-Verlag (1969), 134-145.|1969|
|[Adjointness in Foundations](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1969-adjointness-in-foundations.pdf)|Dialectica 23 (1969), 281-296|1969|
|[Equality in Hyperdoctrines and Comprehension Schema as an Adjoint Functor](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1970-equality-in-hyperdoctrines-and-comprehension-schema-as-an-adjoint-functor.pdf)|Proceedings of the American Mathematical Society Symposium on Pure Mathematics XVII (1970), 1-14|1970|
|[Quantifiers and Sheaves](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1970-quantifiers-and-sheaves.pdf)|Proceedings of the International Congress on Mathematics, Nice 1970, Gauthier-Villars (1971) 329-334|1970|
|[Introduction to "Toposes, Algebraic Geometry and Logic"](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1971-introduction-to-toposes-algebraic-geometry-and-logic.pdf)|Springer Lecture Notes in Mathematics No. 274, New York: Springer, pp. 1–12|1971|
|Closed categories and biclosed bicategories|Mathematics Institute Aarhus Universitet, Aarhus. Handwritten lecture notes|1971|
|[Theory of Categories over a Base Topos](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1972-perugia-lecture-notes.pdf)|Lectures given at Università di Perugia|1972|
|[Metric Spaces, Generalized Logic, and Closed Categories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1973-metric-spaces-generalized-logic-closed-categories.pdf)|Originally published in Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166; Republished in Reprints in TAC, No.1 2002 pp. 1-37|1973|
|Logic of Topoi: inside and outside|Lecture Notes, Université de Montréal|1974|
|[Introduction to "Model Theory & Topoi"](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1975-introduction-to-model-theory-and-topoi.pdf)|Springer Lecture Notes in Mathematics No. 445, Springer-Verlag, pp. 3-14|1975|
|[Variable Sets Etendu and Variable Structure in Topoi](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1975-variable-sets-etendu-and-variable-structure-in-topoi.pdf)|Notes by Steven Landsburg of Lectures and Conversations, Spring 1975, University of Chicago|1975|
|[Continuously Variable Sets – Algebraic Geometry=Geometric Logic](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1975-continuously-variable-sets-algebraic-geometry--geometric-logic.pdf)|Studies in Logic and the Foundations of Mathematics, Volume 80, pp. 135-156|1975|
|[Variable Quantities and Variable Structures in Topoi](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1976-variable-quantities-and-variable-structures-in-topoi.pdf)|Algebra, topology, and category theory (a collection of papers in honor of Samuel Eilenberg), pp. 101–131|1976|
|[Discussion on philosophy (notes)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1978-discussion-on-philosophy.pdf)|Notes by Anders Kock, Aarhus Open House, May 1978|1978|
|[Discussion on geometry (notes)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1978-discussion-on-geometry.pdf)|Notes by Anders Kock, Aarhus Open House, May 1978|1978|
|[Hardy fields (notes)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1978-hardy-fields.pdf)|Notes by Anders Kock, Aarhus Open House, May 1978|1978|
|[Categorical Dynamics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1978-categorical-dynamics.pdf)|Proceedings of Aarhus May 1978 Open House on Topos Theoretic Methods in Geometry|1978|
|[Toward the Description in a Smooth Topos of the Dynamically Possible Motions and Deformations of a Continuous Body](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1980-toward-the-description-in-a-smooth-topos-of-the-dynamically-possible-motions-and-deformations-of-a-continuous-body.pdf)|Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume: 21, Issue: 4, pp. 377-392|1980|
|On C-∞ functions|Preprint, State Univ. of New York, Buffalo|1981|
|[Thermodynamics of deformations of continuous bodies, non homogeneous, with memory, far from equilibrium](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1982-termodinamica-delle-deformazioni-per-sistemi-continui.pdf)|Handwritten notes (in Italian) from a seminar held in Trieste|1982|
|[Review of Cohn, Universal Algebra (second edition)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1982-review-of-cohn-universal-algebra.pdf)|American Scientist|1982|
|[Introduction to "Categories in Continuum Physics"](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1982-introduction-to-categories-in-continuum-physics.pdf)|Springer Lecture Notes in Mathematics No. 1174, Springer-Verlag (1986)|1982|
|Measures on toposes|Proceedings of Aarhus Workshop on Category Theoretic Methods in Geometry|1983|
|[Functorial Remarks on the General Concept of Chaos](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1984-functorial-remarks-on-the-general-concept-of-chaos.pdf)|IMA Research Report #87, University of Minnesota (1986)|1984|
|[State Categories Closed Categories and the Existence of Semi-continuous Entropy Functions](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1984-state-categories-closed-categories-and-the-existence-of-semi-continuous-entropy-functions.pdf)|IMA Research Report #86, University of Minnesota|1984|
|[State Categories and Response Functors](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1986-state-categories-and-response-functors.pdf)|Preprint|1986|
|[Categories of Spaces may not be Generalized Spaces as Exemplified by Directed Graphs](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1986-categories-of-spaces-may-not-be-generalized-spaces-as-exemplified-by-directed-graphs.pdf)|Revista Colombiana de Matemáticas XX (1986), pp. 179-185|1986|
|[Taking Categories Seriously](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1986-taking-categories-seriously.pdf)|Revista Colombiana de Matemáticas XX (1986), pp. 147-178|1986|
|Some "New" Mathematics Arising From the Study of Grassmann 1844|Unpublished manuscript|1987|
|Concepts and Problems in Mathematical Toposes (abstract)|CMS Winter Meeting, December 1988, Toronto, Program p. 31, Special Session on Category Theory|1988|
|Fractional Exponents in Cartesian Closed Categories|Unpublished manuscript|1988|
|Möbius algebra of a category|Handwritten Notes by S. Schanuel at the Sydney Combinatorics Seminar organized by Don Taylor|1988|
|[Toposes generated by codiscrete objects in combinatorial topology and functional analysis](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1989-toposes-generated-by-codiscrete-objects-in-combinatorial-topology-and-functional-analysis.pdf)|TAC Reprint (2021) of notes for Colloquium lectures given at North Ryde, New South Wales, Australia 1988-89|1989|
|[On the Complete Lattice of Essential Localizations (with G.M. Kelly)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1988-on-the-complete-lattice-of-essential-localizations.pdf)|Bull. Société Mathematique de Belgique, XLI, 289-319|1988|
|Intrinsic boundary in certain mathematical toposes exemplify logical operators not passively preserved by substitution|Preprint, Univ. of Buffalo|1989|
|[Display of Graphics and their Applications Exemplifed by 2 Categories and the Hegelian Taco](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1989-display-of-graphics-and-their-applications-exemplifed-by-2-categories-and-the-hegelian-taco.pdf)|Proceedings of the First International Conference on Algebraic Methodology and Software Technology, The University of Iowa, 51-75|1989|
|[Qualitative Distinctions Between Some Toposes of Generalized Graphs](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1989-qualitative-distinctions-between-some-toposes-of-generalized-graphs.pdf)|Proceedings of AMS Boulder 1987 Symposium on Category Theory and Computer Science, Contemporary Mathematics, 261-299|1989|
|[Intrinsic Co-Heyting Boundaries and the Leibniz Rule in Certain Toposes](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1991-intrinsic-co-heyting-boundaries-and-the-leibniz-rule-in-certain-toposes.pdf)|Category Theory, Proceedings Como 1990, A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) pp. 279-281|1991|
|[More on Graphic Toposes](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1991-more-on-graphic-toposes.pdf)|Proceedings of the 1989 Bangor Category Theory Meeting, Cahiers de Topologie et Géométrie Différentielle Catégorique XXXII - 1 (1991), pp. 5-10|1991|
|[Some Thoughts on the Future of Category Theory](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1991-some-thoughts-on-the-future-of-category-theory.pdf)|Category Theory, Proceedings Como 1990. A. Carboni, M. C. Pedicchio, G. Rosolini (Eds). Springer Lecture Notes in Mathematics 1488, Springer-Verlag (1991) pp. 1-13|1991|
|[Categories of Space and Quantity](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1992-categories-of-space-and-quantity.pdf)|The Space of Mathematics: Philosophical, Epistemological and Historical Explorations, International Symposium on Structures in Mathematical Theories (1990), San Sebastian, Spain; DeGruyter, Berlin (1992), pp. 14-30.|1992|
|[Introduction to Linear Categories and Applications](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1992-introduction-to-linear-categories-and-applications.pdf)|Course lecture notes|1992|
|[Cohesive Toposes and Cantor's Lauter Einsen](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1994-cohesive-toposes-and-cantors-lauter-einsen.pdf)|Philosophia Mathematica, The Canadian Society for History and Philosophy of Mathematics, Series III, Vol. 2 (1994), pp. 5-15.|1994|
|[Tools for the Advancement of Objective Logic Closed Categories and Toposes](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1994-tools-for-the-advancement-of-objective-logic-closed-categories-and-toposes.pdf)|The Logical Foundations of Cognition, J. Macnamara, G. E. Reyes (Eds). Oxford University Press (1994), pp. 43-56|1994|
|[Adjoints in and among Bicategories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1996-adjoints-in-and-among-bicategories.pdf)|Logic & Algebra, Proceedings of the 1994 Siena Conference in Memory of Roberto Magari. Lecture Notes in Pure and Applied Algebra 180: pp. 181-189, Ed. Ursini/Aglianò, Marcel Dekker, Inc. Basel, New York|1996|
|[Grassmann's Dialectics and Category Theory](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1996-grassmans-dialectics-and-category-theory.pdf)|Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar pp. 255-264, Boston Studies in the Philosophy of Science Series (BSPS, volume 187)|1996|
|[Unity and Identity of Opposites in Calculus and Physics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1996-unity-and-identity-of-opposites-in-calculus-and-physics.pdf)|Proceedings of ECCT 1994 Tours Conference, Applied Categorical Structures, 4: pp. 167-174 Kluwer Academic Publishers|1996|
|[History and Philosophy of Mathematic Reform](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1996-history-and-philosophy-of-mathematic-reform.pdf)|CPCML Inter-Disciplinary Conference, University of Windsor on 'The Origin of Consciousness and Social Change'|1996|
|Algebra Step by Step|Buffalo Workshop Press, ISBN: 0963180525|1997|
|Conceptual Mathematics (First Edition)|Book with Stephen Schanuel. See Second Edition, 2009|1997|
|Linearization Revisited (Talk)|IIIrd Joint Meeting AMS-SMM, Special Session on Rings and Category Theory, Oaxaca Mexico, December 1997, Program p. 59|1997|
|[Toposes of Laws of Motion](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1997-toposes-of-laws-of-motion.pdf)|Transcript from Video, Montreal September 27, 1997|1997|
|[Volterra's Functionals and Covariant Cohesion of Space](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1997-volterras-functionals-and-covariant-cohesion-of-space.pdf)|Supplemento ai Rendiconti del Circolo Matematico di Palermo, Serie II, 64, R. Betti, F. W. Lawvere (Eds.), (2000), pp. 201-214|1997|
|Everyday physics of extended bodies or why functionals need analyzing (abstract, cf. paper 2017)|Public Lecture, CMS Summer 1998 Meeting, University of New Brunswick, Saint John, June 13-15, (received May 1998)|1998|
|[Outline of Synthetic Differential Geometry](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1998-outline-of-synthetic-differential-geometry.pdf)|Buffalo Geometry Seminar notes, February 1998|1998|
|Are Homotopy Types the Same As Infinitesimal Skeleta? (talk, [abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1998-are-homotopy-types-the-same-as-infinitesimal-skeleta-abstract.pdf))|[CMS Summer 1998 Meeting](https://cms.math.ca/Events/summer98/)|1998|
|Categorical Analyses of the Whole/Part Relation (abstract)|Mitteleuropaeisches Kulturinstitut, Bolzano, Italy|1998|
|Smoothness of Cubical Splines (Talk)|AMS [Special Session on Smooth Categories in Geometry and Mechanics](https://www.ams.org/meetings/sectional/2039_program_ssa.html)|1999|
|[Categorie e Spazio: Un Profilo](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1999-categorie-e-spazio.pdf)|Lettera matematica PRISTEM 31, Springer, Italy, (1999), 35-50. [Reprinted in La Mathematica a cura di Bartocci, Claudio, Giulio Einaudi editore (2010) vol. 4, 107-135.|1999|
|[Kinship and Mathematical Categories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1999-kinship-and-mathematical-categories.pdf)|Language, Logic, and Conceptual Representation, P. Bloom, R. Jackendoff, and K. Wynn (Eds), MIT Press, (1999), pp. 411-425|1999|
|[Comments on the Development of Topos Theory](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2000-comments-on-the-development-of-topos-theory.pdf)|Development of Mathematics 1950-2000, J.-P. Pier (Ed) Birkhäuser Verlag, Basel, (2000), pp. 715-734|2000|
|[The Role of Cartesian Closed Categories in Foundations (Interview with Felice Cardone)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2000-cardone-interview.pdf)||2000|
|[Explicit foundational concepts in the teaching of mathematics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2001-explicit-foundational-concepts-in-the-teaching-of-mathematics.pdf)|Matematica e filosofia: il problema dei fondamenti oggi PRISTEM/Storia 14-15 - Translation: Filsofia, scienza e bioetica nel dibattito contemporaneo a cura di Minazzi, Fabio, Instituto Poligrafico e Zecca dello Stato, Roma|2001|
|[Categorical Algebra for Continuum Micro Physics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2001-categorical-algebra-for-continuum-micro-physics.pdf)|Journal of Pure and Applied algebra 175, (2002), pp. 267-287|2001|
|[Incontro con Ludovico Geymonat Anno 1977](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2003-incontro-con-ludovico-geymonat-anno-1977.pdf)|Fabio Minazzi (ed.), Filosofia, scienza e vita civile nel pensiero di Ludovico Geymonat, La Città del Sole Napoli 2003. pp.181-185|2003|
|[Sets for Mathematics](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2003-sets-for-mathematics.pdf)|Book with Robert Rosebrugh|2003|
|[On the Duality Between Varietes and Algebraic Theories](Https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2003-on-the-duality-between-varieties-and-algebraic-theories.pdf) (with J. Adámek & J. Rosický)|Algebra Universalis, (2003), pp. 35-49|2003|
|[How Algebraic is Algebra?](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2001-how-algebraic-is-algebra.pdf) (with J. Adámek & J. Rosický)|Theory and Applications of Categories , Vol. 11, 2003, No. 11, pp. 252-282|2001|
|[Linearization of Graphic Toposes via Coxeter Groups](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2002-linearization-of-graphic-toposes-via-coxeter-groups.pdf)|Journal of Pure and Applied Algebra, vol. 168, (2002), pp. 425-436|2002|
|[Foundations and Applications – Axiomatization and Education](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2003-foundations-and-applications-axiomatization-and-education.pdf)|The Bulletin of Symbolic Logic, vol. 9, No. 2, (2003), pp. 213-224|2003|
|[Continuous Categories Revisited](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2003-continuous-categories-revisited.pdf) (with J. Adámek & J. Rosický)|Theory and Applications of Categories , Vol. 11, 2003, No. 11, pp 252-282|2003|
|[Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2004-functorial-semantics-of-algebraic-theories-etc.pdf)|Reprints in Theory and Applications of Categories, No. 5 (2004) pp 1-121. Originally published as: Ph.D. thesis, Columbia University, 1963 and in Reports of the Midwest Category Seminar II, 1968, pp. 41-61|2004|
|[Functorial Concepts of Complexity for Finite Automata](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2004-functorial-concepts-of-complexity-for-finite-automata.pdf)|Theory and Applications of Categories, Vol. 13, 2004, No. 10, pp. 164-168|2004|
|[Left and Right Adjoint Operations on Spaces and Data Types](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2004-left-and-right-adjoint-operations-on-spaces-and-data-types.pdf)|For Dana Scott's Seventieth Birthday, Copenhagen 2002, Theoretical Computer Science, Elsevier, vol 316/1-3, (2004) pp. 105-111|2004|
|[An Elementary Theory of the Category of Sets (long version) with commentary](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2005-an-elementary-theory-of-the-category-of-sets-with-commentary.pdf)|Reprints in Theory and Applications of Categories, No. 11 (2005) pp. 1-35. Expanded version of Proceedings of the National Academy of Science of the U.S.A 52, 1506-1511, with commentary by Colin McLarty and the author.|2005|
|[Grassmann Book Reviews](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2005-book-reviews.pdf)|Historia Mathematica, vol. 32, (2005), pp. 101-106|2005|
|[John Isbell's Adequate Subcategories](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2006-john-isbell's-adequate-subcategories.pdf)|[Topological Commentary, Vol. 11 #1](http://at.yorku.ca/t/o/p/d/63.htm)|2006|
|[Review of Anders Kock, Synthetic Differential Geometry (second edition)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2007-review-of-kock-sdg.pdf)|SIAM review|2007|
|[Axiomatic Cohesion](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2007-axiomatic-cohesion.pdf)|Theory and Applications of Categories, online publication, Special volume from the CT2006 Conference at Whitepoint Nova Scotia, vol 19, (2007), 41-49|2007|
|Cohesive toposes: combinatorial and infinitesimal cases ([video](https://www.youtube.com/user/rfcwalters/videos)) ([lecture notes](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2008-cohesive-toposes-combinatorial-and-infinitesimal-cases.pdf))|Lectures in Como (Italy), January 10, 2008|2008|
|[Core Varieties Extensivity and Rig Geometry](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2008-core-varieties-extensivity-and-rig-geometry.pdf)|Theory and Applications of Categories, Vol. 20, 2008, No. 14, pp 497-503.|2008|
|[Interview with Maria Manuel Clementino and Jorge Picado](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2008-picado-interview.pdf)|Bulletin of the International Center for Mathematics (part 1, December 2007, part 2, June 2008)|2008|
|[Foreword To "Algebraic Theories"](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2009-foreword-to-algebraic-theories.pdf)|Cambridge Tracts in Mathematics 184, J. Adámek, J. Rosický & E. M. Vitale (2012)|2009|
|[Conceptual Mathematics (Second Edition)](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2009-conceptual-mathematics-second-edition.pdf)|Book with Stephen Schanuel|2009|
|[Open Problems in Topos Theory](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2009-open-problems-in-topos-theory.pdf)|88th Peripatetic Seminar on Sheaves and Logic, For Martin Hyland and Peter Johnstone in honor of their sixtieth birthdays (updated July 2016)|2009|
|[The Hopf Algebra of Möbius Intervals](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2010-the-hopf-algebra-of-mobius-intervals.pdf) (with M. Menni)|Theory and Applications of Categories, online publication, vol. 24, (2010), 221-265|2010|
|Categorical Dynamics ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2011-categorical-dynamics-abstract.pdf))|Talk at [International Category Theory Conference, Vancouver, July 2011](http://www.mat.uc.pt/~ct2011/)|2011|
|[Euler's Continuum Functorially Vindicated](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2011-euler's-continuum-functorially-vindicated.pdf)|Logic, Mathematics, Philosophy: Vintage Enthusiasms, Essays in Honour of John L. Bell, D. DeVidi et al. (Eds), Western Ontario Series in Philosophy of Science 75, (2011)|2011|
|[What Is A Space? (video)](https://www.youtube.com/watch?v=5_bqD6tTHG8)|[Sets Within Geometry symposium - Nancy, France 26-29 July 2011](http://www.archmathsci.org/conferences-and-workshops/symposium-sets-within-geometry-nancy-france-26-29-july-2011-2/)|2011|
|[The Dialectic of Continuous and Discrete in the History of the Struggle for a Usable Guide to Mathematical Thought (video)](https://www.youtube.com/watch?v=OE-R3565jrs)|[Sets Within Geometry symposium - Nancy, France 26-29 July 2011](http://www.archmathsci.org/conferences-and-workshops/symposium-sets-within-geometry-nancy-france-26-29-july-2011-2/)|2011|
|[Categorical Dynamics Revisited: Category Theory and the Representation of Physical Quantities (video)](https://www.youtube.com/watch?v=sXATg9_6iWE)|[Sets Within Geometry symposium - Nancy, France 26-29 July 2011](http://www.archmathsci.org/conferences-and-workshops/symposium-sets-within-geometry-nancy-france-26-29-july-2011-2/)|2011|
|What are Foundations of Geometry and Algebra? ([abstract](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2013-what-are-foundations-of-geometry-and-algebra.pdf) ([video](https://www.youtube.com/watch?v=ZYGyEPXu8as)) ([transcript](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2013-fifty-years-of-functorial-semantics-transcript.pdf))|[Fifty Years of Functorial Semantics Conference](http://www.math.union.edu/~niefiels/13conference/Web/)|2013|
|[Internal Choice Holds in the Discrete Part of any Cohesive Topos Satisfying Stable Connected Codiscreteness](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2015-internal-choice-holds-in-the-discrete-part-of-any-cohesive-topos-satisfying-stable-connected-codiscreteness.pdf) (with M. Menni)|Theory and Applications of Categories, online publication, vol. 30, (2015), No. 26, pp 909-932|2015|
|[Alexander Grothendieck and the Concept of Space](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2015-alexander-grothendieck-and-the-concept-of-space.pdf)|Invited address at CT 2015 Aveiro, Portugal|2015|
|[Birkhoff's Theorem from a Geometric Perspective: A Simple Example](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2016-birkhoffs-theorem-from-a-geometric-perspective-a-simple-example.pdf)|Categories and General Algebraic Structures with Apllications Vol. 4, no. 1, (2016), pp. 1-7|2016|
|[Everyday physics of extended bodies or why functionals need analyzing](https://github.com/mattearnshaw/lawvere/blob/master/pdfs/2017-everyday-physics-of-extended-bodies-or-why-functionals-need-analyzing.pdf)|[Categories and General Algebraic Structures with Applications, Volume 6 2017, pp. 9-19](http://www.cgasa.ir/volume_3074.html)|2017|