\setlength{\parindent}{0pt} \setlength{\parskip}{1em} \DeclareMathOperator{\obinternal}{ob} \DeclareMathOperator{\morinternal}{mor} \DeclareMathOperator{\dominternal}{dom} \DeclareMathOperator{\codinternal}{cod} \renewcommand\ob{\glsref[category_symbol]{\obinternal}} \newcommand\mor{\glsref[category_symbol]{\morinternal}} \newcommand\dom{\glsref[category_symbol]{\dominternal}} \newcommand\cod{\glsref[category_symbol]{\codinternal}} \newcommand\Set{\glsref[catexamples_symbol]{\mathbf{Set}}} \newcommand\Gp{\glsref[catexamples_symbol]{\mathbf{Gp}}} \newcommand\Rng{\glsref[catexamples_symbol]{\mathbf{Rng}}} \newcommand\Vect{\glsref[catexamples_symbol]{\mathbf{Vect}}} \newcommand\Top{\glsref[catexamples_symbol]{\mathbf{Top}}} \newcommand\Met{\glsref[catexamples_symbol]{\mathbf{Met}}} \newcommand\Mfd{\glsref[catexamples_symbol]{\mathbf{Mfd}}} \newcommand\Htpy{\glsref[catexamples_symbol]{\mathbf{Htpy}}} \newcommand\Rel{\glsref[catexamples_symbol]{\mathbf{Rel}}} \newcommand\Part{\glsref[catexamples_symbol]{\mathbf{Part}}} \renewcommand\Mat{\glsref[catexamples_symbol]{\mathbf{Mat}}} \newcommand\op{{\glsref[opcat_symbol]{{\mathrm{op}}}}} \newcommand\Cat{\glsref[Cat_symbol]{\mathbf{Cat}}} \newcommand\twofuncs[2]{ \!\!\!\! \raisebox{0.2em}{ \adjustbox{scale=0.6}{ \begin{tikzcd}[ampersand replacement=\&] \phantom{} \ar[shift left=3pt, r, "#1"] \ar[shift right=3pt, r, swap, "#2"] \& \phantom{} \end{tikzcd} } } \!\!\!\! } \def\funccat[#1, #2]{\glsref[funccat_symbol]{[#1, #2]}} \newcommand\identity[1]{1_{#1}} \newcommand\equivc{\glsref[equiv_symbol]{\equiv}} \newcommand\partf{\rightharpoondown} \newcommand\congarrow{\stackrel[\cong]{}{\to}} \newcommand\epic{\glsref[monoepi_symbol]{\twoheadrightarrow}} \newcommand\monic{\glsref[monoepi_symbol]{\rightarrowtail}} \def\morphs#1(#2,#3){\glsref[morphs_symbol]{#1(#2, #3)}} \def\morphf#1(#2,#3){\glsref[morphf_symbol]{#1(#2, #3)}} \newcommand\adjoint{\glsref[adjoint_symbol]{\dashv}} \newcommand\darr{\glsref[darr_symbol]{\downarrow}} \newcommand\funcslr[2]{ \!\!\!\! \raisebox{0.2em}{ \adjustbox{scale=0.6}{ \begin{tikzcd}[ampersand replacement=\&] \phantom{} \ar[shift left=3pt, r, "#1"] \& \phantom{} \ar[shift left=3pt, l, "#2"] \end{tikzcd} } } \!\!\!\! } % \newcommand\funcslr[2]{\underset{\scriptscriptstyle #2}{\overset{\scriptscriptstyle #1}{\rightleftarrows}}} \newcommand\AbGp{\mathbf{AbGp}} \newcommand\KHaus{\mathbf{KHaus}} \newcommand\Lat{\mathbf{Lat}} \newcommand\CLat{\mathbf{CLat}} \newcommand\CSLat{\mathbf{CSLat}} \newcommand\DLat{\mathbf{DLat}} \newcommand\tfAbGp{\mathbf{tfAbGp}} \newcommand\Mod{\mathbf{Mod}} \newcommand\Cone{\glsref[cone_symbol]{\mathbf{Cone}}} \newcommand\Diag{\glsref[Deltadiag_symbol]{\Delta}} \DeclareMathOperator{\Subinternal}{Sub} \newcommand\Sub{\glsref[Sub_symbol]{\Subinternal}} \newcommand\suble{\glsref[Sub_symbol]{\le}} \newcommand\Tbb{\glsref[monad]{\mathbb{T}}} \newcommand\EMaT{\glsref[EMaT_symbol]{^{\mathbb{T}}}} \newcommand\emat{\glsref[EMaT_symbol]{^{\mathbb{T}}}} \newcommand\kct{\glsref[KcT_symbol]{_{\mathbb{T}}}} \newcommand\kto[1][]{{\color{red} \stackrel{#1}{\to}}} \newcommand\kar[1][]{\ar[#1, red]} \DeclareMathOperator{\Adjinternal}{Adj} \newcommand\Adj{\glsref[Adj_symbol]{\Adjinternal}} \newcommand\gsplit[1]{\glsref[gsplit]{$#1$-split}} \newcommand\colim{\operatorname*{colim}} \newcommand\Setf{\glsref[Setf_symbol]{\mathbf{Set}_f}} \newcommand\covers{\glsref[cover_symbol]{\rightarrowtriangle}} \newcommand\torel{\glsref[relation_symbol]{\looparrowright}} \newcommand\Reln{\glsref[Relc_symbol]{\mathbf{Rel}}} \newcommand\bull{{\glsref[bull_symbol]{\bullet}}} \newcommand\ucirc{{\glsref[circ_symbol]{\circ}}} \newcommand\ws{{\glsref[ws_symbol]{\text{ws}}}} \newcommand\tv{{\glsref[tv_symbol]{\text{tv}}}} \let\customstackrel\stackrel