\relax 
\providecommand\hyper@newdestlabel[2]{}
\@writefile{toc}{\contentsline {chapter}{\numberline {0}Introduction}{3}{chapter.0}\protected@file@percent }
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\newlabel{chap:intro}{{0}{3}{Introduction}{chapter.0}{}}
\newlabel{chap:intro@cref}{{[chapter][0][]0}{[1][3][]3}}
\@writefile{toc}{\contentsline {section}{\numberline {0.1}Appetizer: inverses in group objects}{3}{section.0.1}\protected@file@percent }
\newlabel{sec:intro}{{0.1}{3}{Appetizer: inverses in group objects}{section.0.1}{}}
\newlabel{sec:intro@cref}{{[section][1][0]0.1}{[1][3][]3}}
\newlabel{eq:invuniq-easy}{{0.1.2}{3}{Appetizer: inverses in group objects}{equation.0.1.2}{}}
\newlabel{eq:invuniq-easy@cref}{{[equation][2][0,1]0.1.2}{[1][3][]3}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Uniqueness of inverses by diagram chasing}}{4}{figure.0.1}\protected@file@percent }
\newlabel{fig:uniqinv-diagram}{{1}{4}{Uniqueness of inverses by diagram chasing}{figure.0.1}{}}
\newlabel{fig:uniqinv-diagram@cref}{{[figure][1][0]1}{[1][4][]4}}
\newlabel{eq:pointwise-unique-inverses}{{0.1.5}{6}{Appetizer: inverses in group objects}{equation.0.1.5}{}}
\newlabel{eq:pointwise-unique-inverses@cref}{{[equation][5][0,1]0.1.5}{[1][6][]6}}
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Monoids and comonoids}}{8}{figure.0.2}\protected@file@percent }
\newlabel{fig:intro-prop-moncomon}{{2}{8}{Monoids and comonoids}{figure.0.2}{}}
\newlabel{fig:intro-prop-moncomon@cref}{{[figure][2][0]2}{[1][7][]8}}
\newlabel{ex:cartmon-bimon-uniq}{{0.1.1}{9}{}{@ex.0.1.1}{}}
\newlabel{ex:cartmon-bimon-uniq@cref}{{[@ex][1][0,1]0.1.1}{[1][9][]9}}
\newlabel{ex:ccmon-cart}{{0.1.2}{9}{}{@ex.0.1.2}{}}
\newlabel{ex:ccmon-cart@cref}{{[@ex][2][0,1]0.1.2}{[1][9][]9}}
\newlabel{ex:antipode}{{0.1.3}{9}{}{@ex.0.1.3}{}}
\newlabel{ex:antipode@cref}{{[@ex][3][0,1]0.1.3}{[1][9][]9}}
\newlabel{ex:eckmann-hilton}{{0.1.4}{9}{}{@ex.0.1.4}{}}
\newlabel{ex:eckmann-hilton@cref}{{[@ex][4][0,1]0.1.4}{[1][9][]9}}
\newlabel{ex:near-ring}{{0.1.5}{9}{}{@ex.0.1.5}{}}
\newlabel{ex:near-ring@cref}{{[@ex][5][0,1]0.1.5}{[1][9][]9}}
\@writefile{toc}{\contentsline {section}{\numberline {0.2}On syntax and free objects}{9}{section.0.2}\protected@file@percent }
\newlabel{sec:syntax}{{0.2}{9}{On syntax and free objects}{section.0.2}{}}
\newlabel{sec:syntax@cref}{{[section][2][0]0.2}{[1][9][]9}}
\newlabel{thm:intro-conjugation}{{0.2.1}{10}{}{thm.0.2.1}{}}
\newlabel{thm:intro-conjugation@cref}{{[thm][1][0,2]0.2.1}{[1][9][]10}}
\citation{js:geom-tenscalc-i}
\citation{selinger:graphical}
\@writefile{brf}{\backcite{js:geom-tenscalc-i,selinger:graphical}{{12}{0.2.2}{rmk.0.2.2}}}
\citation{mr:focl}
\citation{ls:hocl}
\citation{jacobs:cltt}
\citation{goldblatt:topoi}
\citation{ptj:elephant}
\newlabel{ex:group-cutadm}{{0.2.1}{13}{}{@ex.0.2.1}{}}
\newlabel{ex:group-cutadm@cref}{{[@ex][1][0,2]0.2.1}{[1][13][]13}}
\@writefile{toc}{\contentsline {section}{\numberline {0.3}On type theory and category theory}{13}{section.0.3}\protected@file@percent }
\newlabel{sec:generalities}{{0.3}{13}{On type theory and category theory}{section.0.3}{}}
\newlabel{sec:generalities@cref}{{[section][3][0]0.3}{[1][13][]13}}
\@writefile{brf}{\backcite{mr:focl,ls:hocl,jacobs:cltt,goldblatt:topoi,ptj:elephant}{{13}{0.3}{section.0.3}}}
\citation{dosen:cutelim-cats}
\@writefile{brf}{\backcite{dosen:cutelim-cats}{{14}{0.3}{section.0.3}}}
\citation{lambek:dedsys-ii}
\citation{burroni:t-cats}
\citation{leinster:higher-opds}
\citation{hermida:coh-univ}
\citation{cs:multicats}
\@writefile{brf}{\backcite{lambek:dedsys-ii}{{16}{0.3}{section.0.3}}}
\@writefile{brf}{\backcite{burroni:t-cats,leinster:higher-opds,hermida:coh-univ,cs:multicats}{{16}{0.3}{section.0.3}}}
\citation{maclane}
\citation{awodey:cat-thy}
\citation{mclarty:ecat-etop}
\citation{leinster:cat-thy}
\citation{leinster:higher-opds}
\citation{cs:multicats}
\citation{mm:shv-gl}
\citation{ptj:topos-theory}
\citation{ptj:elephant}
\citation{jacobs:cltt}
\@writefile{toc}{\contentsline {section}{\numberline {0.4}Expectations of the reader}{17}{section.0.4}\protected@file@percent }
\newlabel{sec:expectations}{{0.4}{17}{Expectations of the reader}{section.0.4}{}}
\newlabel{sec:expectations@cref}{{[section][4][0]0.4}{[1][16][]17}}
\@writefile{brf}{\backcite{maclane,awodey:cat-thy,mclarty:ecat-etop,leinster:cat-thy}{{17}{0.4}{section.0.4}}}
\@writefile{brf}{\backcite{leinster:higher-opds,cs:multicats}{{17}{0.4}{section.0.4}}}
\@writefile{brf}{\backcite{mm:shv-gl,ptj:topos-theory,ptj:elephant,jacobs:cltt}{{17}{0.4}{section.0.4}}}
\@setckpt{intro}{
\setcounter{page}{18}
\setcounter{equation}{0}
\setcounter{enumi}{4}
\setcounter{enumii}{0}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{2}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{0}
\setcounter{section}{4}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{2}
\setcounter{table}{0}
\setcounter{parentequation}{0}
\setcounter{section@level}{1}
\setcounter{Item}{6}
\setcounter{Hfootnote}{2}
\setcounter{bookmark@seq@number}{6}
\setcounter{thm}{0}
\setcounter{@ex}{0}
}