% \iffalse meta-comment % % Copyright (C) 2018 - 2021 by ChairX % % This file may be distributed and/or modified under the % conditions of the LaTeX Project Public License, either % version 1.3 of this license or (at your option) any later % version. The latest version of this license is in: % % http://www.latex-project.org/lppl.txt % % and version 1.3 or later is part of all distributions of % LaTeX version 2005/12/01 or later. % % This file contains the documentation of all category theory related macros . % % Macros have to be described by (delete the first %) % \DescribeMacro{\macro} % Description and usage of the macro. % % The description will appear in the usage % part of the documentation. Use \subsubsection{} etc. for structuring. % % The implementation of the macros defined here has to be written in % chairxmathCategory.dtx %\fi % % % \subsubsection{General Category Theory} % % \DescribeMacro{\category} % Font for generic categories |\category{C}|: $\category{C}$ \\ % Uses |categoryfont|. % % \DescribeMacro{\categoryname} % Font for specific categories |\categoryname{FinSet}|: $\categoryname{FinSet}$ \\ % Uses |categorynamefont|. % % \DescribeMacro{\functor} % Font for functors |\functor{F}|: $\functor{F}$ \\ % Uses |functorfont|. % % \DescribeMacro{\groupoid} % Font for groupoids |\groupoid{G}|: $\groupoid{G}$ \\ % Uses |groupoidfont|. % % \DescribeMacro{\source} % Source of arrow |\source(f)|: $\source(f)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\target} % Target of arrow |\target(f)|: $\target(f)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\unit} % Unit map in groupoids |\unit\colon M \longrightarrow G|: % $\unit\colon M \longrightarrow G$ \\ % Uses |operatorfont|. % %\DescribeMacro{\opp} % Opposite category etc. |\category{C}^\opp|: $\category{C}^\opp$ \\ % Uses |scriptfont|. % % \DescribeMacro{\asso} % Natural transformation of associativity |\asso|: $\asso$ \\ % Uses |operatorfont|. % % \DescribeMacro{\Hom} % Homomorphisms |\Hom(A, B)|: $\Hom(A, B)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\End} % Endomorphisms |\End(E)|: $\End(E)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\Aut} % ($*$-)Automorphisms |\Aut(A)|: $\Aut(A)$ \\ % |\Aut*(A)|: $\Aut*(A)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\Iso} % ($*$-)Isomorphisms |\Iso(A, B)|: $\Iso(A, B)$ \\ % |\Iso*(A, B)|: $\Iso*(A, B)$ \\ % Uses |operatorfont|. % % \DescribeMacro{\Obj} % Objects of a category |\Obj(\category{C})|: $\Obj(\category{C})$ \\ % Uses |operatorfont|. % % \DescribeMacro{\Morph} % Morphisms of a category |\Morph(a, b)|: $\Morph(a, b)$ \\ % Uses |operatorfont|. % % \subsubsection{Colimits} % %\DescribeMacro{\colim} % Colimits of diagrams or functors: |\colim \functor{F}|: $\colim \functor{F}$