blob: 5eb3e791a2729cbcf9439ed45c7f612929e5f543 (
plain)
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
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
|
\documentclass[11pt,twoside]{amsbook}
% Style
\usepackage[utf8]{inputenc}
\usepackage[spanish]{babel}
\usepackage{microtype}
\usepackage[a4paper,width=150mm,top=25mm,bottom=25mm,bindingoffset=6mm]{geometry}
\usepackage{fancyhdr}
\pagestyle{fancy}
% \renewcommand{\headrulewidth}{0.4pt}
% \renewcommand{\footrulewidth}{0.4pt}
% Bibliography
\usepackage[autolang=hyphen]{biblatex}
\addbibresource{ref.bib}
% Formatting
\usepackage{caption}
\usepackage{subcaption}
\usepackage{tikz}
% Math packages
\usepackage{mathtools}
\usepackage{amsthm}
\usepackage{amssymb}
% Theorem styles
\theoremstyle{definition}
\newtheorem{definition}{Definición}
\theoremstyle{remark}
\newtheorem{example}{Ejemplo}
% Math macros
\newcommand{\dash}{\text{-}}
\newcommand{\dCat}[2]{\newcommand{#1}{{\bf #2}}}
\newcommand{\conc}[1]{\emph{#1}}
\dCat{\bAlg}{Alg}
\dCat{\bSet}{Set}
\dCat{\bRel}{Rel}
\dCat{\bPrord}{Prord}
\dCat{\bOrd}{Ord}
\dCat{\bLat}{Lat}
\dCat{\bGrph}{Grph}
\dCat{\bMat}{Mat}
\dCat{\bSmgrp}{Smgrp}
\dCat{\bMon}{Mon}
\dCat{\bGrp}{Grp}
\dCat{\bAb}{Ab}
\dCat{\bRing}{Ring}
\dCat{\bField}{Field}
\dCat{\bMod}{Mod}
\dCat{\bVec}{Vec}
\dCat{\bTop}{Top}
\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}
\newcommand{\cB}{\mathcal{B}}
\newcommand{\cC}{\mathcal{C}}
\newcommand{\cD}{\mathcal{D}}
\newcommand{\dKey}[2]{\newcommand{#1}{\text{#2}}}
\newcommand{\dKeyPar}[2]{\newcommand{#1}[1]{\text{#2}({##1})}}
\dKeyPar{\Ob}{Ob}
\dKeyPar{\Mor}{Mor}
\dKey{\dom}{dom}
\dKey{\cod}{cod}
\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}
\begin{document}
\begin{titlepage}
\begin{center}
\vspace*{1cm}
\Huge
\textbf{Teoría de Categorías}
\vspace{0.5cm}
\LARGE
Una visión general con aplicaciones a la computación
\vspace{1.5cm}
\textbf{Juan Marín Noguera}
\vfill
{\normalsize (Dibujo aquí)} % TODO
\vfill
Trabajo Fin de Grado en Matemáticas
\vspace{0.8cm}
\Large
Tutor: Alberto del Valle Robles\\
Facultad de Matemáticas\\
Universidad de Murcia\\
Día de Mes de 2023 % TODO
\end{center}
\end{titlepage}
\tableofcontents
\listoffigures
\listoftables
\begin{otherlanguage}{english}
\chapter*{Introduction}
% TODO
%\cite{joyofcats}
%\cite{maclane}
\end{otherlanguage}
\chapter{Categorías}
\input{ch1_cats}
\chapter{Funtores}
% TODO
\chapter{Límites}
% TODO
\chapter{Transformaciones naturales}
% TODO
\chapter{Adjunciones}
% TODO
\chapter{Mónadas}
% TODO
\appendix
%\chapter{Bibliografía}
% ... BibTeX stuff here
\printbibliography
\end{document}
%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End:
|
