1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
|
\usepackage[utf8]{inputenc}
\usepackage[english,spanish]{babel}
\usepackage{microtype}
%\renewcommand{\fullwidthdisplay}{}
% Formatting
\usepackage{tikz}
\newenvironment{diagram}{\begin{tikzpicture}\selectlanguage{english}}{\end{tikzpicture}}
\usetikzlibrary{decorations.pathmorphing}
\newcommand{\tikzsquig}{\draw[->,
line join=round,
decorate, decoration={
zigzag,
segment length=4,
amplitude=.9,post=lineto,
post length=2pt
}]} % https://tex.stackexchange.com/questions/12678/squiggly-arrows-in-tikz#12680
% Math packages
\usepackage{mathtools}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{stackrel}
% Theorem styles
%\newtheorem{proposition}{Proposición}[chapter]
%\newtheorem{theorem}[proposition]{Teorema}
%\newtheorem{corollary}[proposition]{Corolario}
%\newtheorem{lemma}[proposition]{Lema}
%\theoremstyle{definition}
%\newtheorem{definition}[proposition]{Definición}
%\newtheorem{axiom}[proposition]{Axioma}
%\theoremstyle{remark}
%\newtheorem{example}[proposition]{Ejemplo}
% Math macros
\newcommand{\E}{\text{e}}
\newcommand{\I}{\text{i}}
\newcommand{\dash}{\text{-}}
\newcommand{\dCat}[2]{\newcommand{#1}{{\bf #2}}}
\newcommand{\conc}[1]{\emph{#1}\newglossaryentry{#1}{name=#1,description={\,}}}
\newcommand{\concsuffix}[1]{\emph{#1}}
\newcommand{\eps}{\varepsilon}
\dCat{\bAlg}{Alg}
\dCat{\bSet}{Set}
\dCat{\bRel}{Rel}
\dCat{\bPrord}{Prord}
\dCat{\bOrd}{Ord}
\dCat{\bLat}{Lat}
\dCat{\bGrph}{Grph}
\dCat{\bMGrph}{MGrph}
\dCat{\bMat}{Mat}
\dCat{\bSmgrp}{Smgrp}
\dCat{\bMon}{Mon}
\dCat{\bGrp}{Grp}
\dCat{\bAb}{Ab}
\dCat{\bRing}{Rng} % Backwards compat
\dCat{\bRng}{Rng}
\dCat{\bCRng}{CRng}
\dCat{\bDom}{Dom}
\dCat{\bField}{Field}
\dCat{\bMod}{Mod}
\dCat{\bVec}{Vec}
\dCat{\bVecf}{Vec_f}
\dCat{\bTop}{Top}
\dCat{\bTopm}{Top_m}
\dCat{\bMetc}{Met_c}
\dCat{\bMetu}{Met_u}
\dCat{\bMet}{Met}
\dCat{\bBanu}{Ban}
\dCat{\bBan}{Ban}
\dCat{\bBanb}{Ban_b}
\dCat{\bZero}{0}
\dCat{\bOne}{1}
\dCat{\bTwo}{2}
\dCat{\bDown}{\downarrow}
\dCat{\bDDown}{\downdownarrows}
\dCat{\bCat}{Cat}
\dCat{\bCAT}{CAT}
\dCat{\bCls}{Cls}
\dCat{\bTopVec}{TopVec}
\dCat{\bType}{Type}
\newcommand{\cA}{\mathcal{A}}
\newcommand{\cB}{\mathcal{B}}
\newcommand{\cC}{\mathcal{C}}
\newcommand{\cD}{\mathcal{D}}
\newcommand{\cS}{\mathcal{S}}
\newcommand{\dKey}[2]{\newcommand{#1}{\text{#2}}}
\newcommand{\dKeyPar}[2]{\newcommand{#1}[1]{\text{#2}({##1})}}
\dKeyPar{\Ob}{Ob}
\dKeyPar{\Mor}{Mor}
\dKeyPar{\Mnd}{Mnd}
\dKey{\dom}{dom}
\dKey{\cod}{cod}
\dKey{\Img}{Im\,}
\newcommand{\dStdSet}[2]{\newcommand{#1}{\mathbb{#2}}}
\dStdSet{\sNat}{N}
\dStdSet{\sInt}{Z}
\dStdSet{\sRat}{Q}
\dStdSet{\sReal}{R}
\dStdSet{\sComplex}{C}
\dStdSet{\sCirc}{S}
\dStdSet{\sTorus}{T}
\newcommand{\monicTo}{\rightarrowtail}
\newcommand{\epicTo}{\twoheadrightarrow}
\newcommand{\inTo}{\hookrightarrow}
\renewcommand{\mapsto}{\rightsquigarrow}
\renewcommand{\Im}{\error{You probably meant \backslash{}Img}}
\newcommand{\dual}[1]{#1^{\mathrm{op}}}
\newcommand{\power}{\mathcal{P}}
\newcommand{\copower}{\mathcal{Q}}
\newcommand{\UNIVERSE}{\mathcal{U}}
\newcommand{\natg}[3]{%
\stackrel[#3]{#2}{\overrightarrow{\underrightarrow{\;{#1}\;}}}}
\newcommand{\nats}[1]{\natg{\downarrow\,{#1}}{}{}}
\newcommand{\nati}[1]{\natg{\cong\,{#1}}{}{}}
\newcommand{\nattwog}[4]{%
\stackrel[#4]{#3}{\overrightarrow{\underrightarrow{%
\xrightarrow[\;{#2}\hfil]{\;{#1}\hfil}}}}}
\newcommand{\nattwos}[2]{\nattwog{\downarrow\,{#1}}{\downarrow\,{#2}}{}{}}
\newcommand{\nattwoi}[2]{\nattwog{\cong\,{#1}}{\cong\,{#2}}{}{}}
\newcommand{\logicrule}[2]{\frac{\displaystyle{#1}}{\displaystyle{#2}}}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
|