Master thesis on Rational Homotopy Theory
https://github.com/Jaxan/Rational-Homotopy-Theory
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95 lines
2.9 KiB
95 lines
2.9 KiB
% -*- root: thesis.tex -*-
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% clickable tocs
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\usepackage{hyperref}
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% use english
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\usepackage[english, british]{babel}
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% floating figures
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\usepackage{float}
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\usepackage{tikz}
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\usetikzlibrary{matrix, arrows, decorations}
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\tikzset{node distance=2.5em, row sep=2.2em, column sep=2.7em, auto}
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\usepackage{graphicx}
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\graphicspath{ {./images/} }
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\usepackage{caption}
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\usepackage{subcaption}
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% Matrices have a upper bound for its size
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\setcounter{MaxMatrixCols}{20}
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% Remove trailing `contents` after toc
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\renewcommand{\contentsname}{}
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% for the fib arrow
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\usepackage{amssymb}
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% mathbb for lowercase bbs
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\usepackage{bbm}
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% Some basic objects
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\newcommand{\N}{\mathbb{N}} % natural numbers
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\newcommand{\Np}{{\mathbb{N}^{>0}}} % positive numbers
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\newcommand{\Z}{\mathbb{Z}} % integers
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\newcommand{\R}{\mathbb{R}} % reals
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\renewcommand{\k}{\mathbbm{k}} % default ground ring
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% Basic category stuff
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\newcommand{\cat}[1]{\mathbf{#1}} % the category of ...
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\newcommand{\Hom}{\mathbf{Hom}}
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\newcommand{\id}{\mathbf{id}}
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% Categories
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\newcommand{\Set}{\cat{Set}} % sets
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\newcommand{\sSet}{\cat{sSet}} % simplicial sets
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\newcommand{\Top}{\cat{Top}} % topological spaces
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\newcommand{\DELTA}{\cat{\Delta}} % the simplicial cat
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\newcommand{\grMod}[1]{\cat{gr\mbox{-}{#1}Mod}} % graded modules over a ring
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\newcommand{\grAlg}[1]{\cat{gr\mbox{-}{#1}Alg}} % graded algebras over a ring
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\newcommand{\DGA}{\cat{DGA}} % differential graded algebras
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\newcommand{\CDGA}{\cat{CDGA}} % commutative dgas
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\newcommand{\cof}{\hookrightarrow} % cofibration
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\newcommand{\fib}{\twoheadrightarrow} % fibration
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\newcommand{\we}{\tot{\simeq}} % weak equivalence
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% Notation and operators
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\newcommand{\I}{\,\mid\,} % seperator in set notation
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\newcommand{\del}{\partial} % boundary
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\newcommand{\iso}{\cong} % isomorphic
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\newcommand{\eq}{\sim} % homotopic
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\newcommand{\tot}[1]{\xrightarrow{\,\,{#1}\,\,}} % arrow with name
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\newcommand{\mapstot}[1]{\xmapsto{\,\,{#1}\,\,}} % mapsto with name
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\DeclareMathOperator*{\colim}{colim}
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\DeclareMathOperator*{\tensor}{\otimes}
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\DeclareMathOperator*{\bigtensor}{\bigotimes}
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\renewcommand{\deg}[1]{{|{#1}|}}
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% restriction of a function
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\newcommand\restr[2]{{% we make the whole thing an ordinary symbol
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\left.\kern-\nulldelimiterspace % automatically resize the bar with \right
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#1 % the function
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\vphantom{\big|} % pretend it's a little taller at normal size
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\right|_{#2} % this is the delimiter
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}}
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% todos
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\newcommand{\todo}[1]{
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\addcontentsline{tdo}{todo}{\protect{#1}}
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$\ast$ \marginpar{\tiny $\ast$ #1}
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}
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\theoremstyle{plain}
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\newtheorem{theorem}{Theorem}[section]
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\newtheorem{proposition}[theorem]{Proposition}
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\newtheorem{lemma}[theorem]{Lemma}
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\newtheorem{corollary}[theorem]{Corollary}
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\theoremstyle{definition}
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\newtheorem{definition}[theorem]{Definition}
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\newtheorem{example}[theorem]{Example}
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% headings for a table
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\newcommand*{\thead}[1]{\multicolumn{1}{c}{\bfseries #1}}
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