latex-setup

My personal LaTeX setup 🦁️⚙️

functional.sty (4138B)

 1 \NeedsTeXFormat{LaTeX2e}[1994/06/01]
 2 \ProvidesPackage{functional}
 3   [2020/09/10 1.0.0 Usefull definitions for Category Theory]
 4 
 5 \RequirePackage{amssymb}
 6 \RequirePackage{amsmath}   % For the \DeclareMathOperator
 7 \RequirePackage{extarrows} % For \xlongrightarrow
 8 \RequirePackage{xfrac}     % For \sfrac
 9 \RequirePackage{relsize}   % For \mathlarger
10 
11 % Define symbols for categories
12 \newcommand{\categoryname}[1]{\ensuremath{\mathbf{#1}}}
13 \newcommand{\newcategory}[2]{\newcommand{#1}{\categoryname{#2}}}
14 \newcommand{\renewcategory}[2]{\renewcommand{#1}{\categoryname{#2}}}
15 
16 % Generic stuff
17 \DeclareMathOperator{\Obj}{Obj}     % The class of objects of a category
18 \DeclareMathOperator{\Hom}{Hom}     % The class of morphisms of a category
19 \DeclareMathOperator{\End}{End}     % Endomorphisms
20 \DeclareMathOperator{\Aut}{Aut}     % Automorphisms
21 \DeclareMathOperator{\coker}{coker} % Cokernel
22 \newcommand{\normal}{\triangleleft} % A normal subobject in a pointed cathegory
23 \newcommand{\op}{\mathrm{op}}       % Dual category
24 \newcommand{\isoto}
25   {\xlongrightarrow{\sim}}          % Isomorphism arrow
26 \newcommand{\mfrac}[2]
27   {\mathlarger{\sfrac{#1}{#2}}}     % Quotient object
28 \newcommand{\wfrac}[2]
29   {\mathlarger{_{#2}\mkern-.5mu\backslash\mkern-2mu^{#1}}} % Quotient object
30 
31 % Function stuff
32 \DeclareMathOperator{\dom}{dom}     % The domain of a morphism
33 \DeclareMathOperator{\codom}{codom} % The codomain of a morphism
34 \DeclareMathOperator{\im}{im}       % The image of morphism
35 \DeclareMathOperator{\id}{id}       % Identity function
36 \newcommand{\To}{\Rightarrow}       % Natural transformation
37 \newcommand{\ot}{\leftarrow}        % Reversed morphism
38 \newcommand{\Ot}{\Leftarrow}        % Reversed natural transformation
39 \newcommand{\fmapsto}[1]
40   {\overset{#1}{\longmapsto}}       % Map declaration
41 
42 % Notable categories
43 \newcategory{\Set}{Set}       % The category of sets
44 \newcategory{\Grp}{Grp}       % The category of groups
45 \newcategory{\FinGrp}{FinGrp} % The category of finite abelian groups
46 \newcategory{\Ab}{Ab}         % The category of abelian groups
47 \newcategory{\FinAb}{FinAb}   % The category of finite abelian groups
48 \newcategory{\Ring}{Ring}     % The category of rings
49 \newcategory{\CRing}{CRing}   % The category of commutative rings
50 \newcategory{\Meas}{Meas}     % The category of measurable spaces
51 \newcategory{\Top}{Top}       % The category of topological spaces
52 \newcategory{\Haus}{Haus}     % The category of Hausdorf spaces
53 \newcategory{\KHaus}{KHaus}   % The category of compact Hausdorf spaces
54 \newcategory{\LCHaus}{LCHaus} % The category of locally compact Hausdorf spaces
55 \newcategory{\GrpTop}{GrpTop} % The category of topological groups
56 \newcategory{\LCGpr}{LCGpr}   % The category of locally compact groups
57 \newcategory{\LCAb}{LCAb}     % The category of locally compact abelian groups
58 \newcategory{\CAb}{CAb}       % The category of compact abelian groups
59 \newcategory{\Mfd}{Mfd}       % The category of smooth manifilds
60 \newcategory{\LieGrp}{LieGrp} % The category of Lie groups
61 \newcategory{\LieAlg}{LieAlg} % The category of Lie algebras
62 \newcategory{\Graph}{Graph}   % The category of graphs
63 \newcategory{\Quiv}{Quiv}     % The category of quivers
64 \newcategory{\PSh}{PSh}       % The category of presheafs over some category
65 \newcategory{\Sh}{Sh}         % The category of sheafs over some site
66 \newcategory{\Bun}{Bun}       % The category of principal G-bundles over some
67                               % manifold
68 \newcategory{\Rep}{Rep}       % The category of representations of an object
69 \newcategory{\rep}{rep}       % The category of finite-dimensional 
70                               % representations of an object
71 \newcategory{\Cat}{Cat}       % The category of (small) categories
72 % The category of vector spaces over a (parameterized) field
73 \newcommand{\Vect}[1]
74   {\ensuremath{#1\operatorname{-}\!\categoryname{Vect}}}
75 % The category of modules over a (parameterized) ring
76 \newcommand{\Mod}[1]
77   {\ensuremath{#1\operatorname{-}\!\categoryname{Mod}}}
78 % The category of algebras over a (parameterized) field
79 \newcommand{\Alg}[1]
80   {\ensuremath{#1\operatorname{-}\!\categoryname{Alg}}}
81 
82 \endinput