Master thesis on Rational Homotopy Theory https://github.com/Jaxan/Rational-Homotopy-Theory
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% normally included with amsart
% \usepackage{amsmath, amsthm}
% font with unicode support, does not work with classicthesis
% \usepackage{fontspec}
% clickable tocs
\usepackage{hyperref}
% floating figures
\usepackage{float}
% for multiple cites
\usepackage{cite}
% fancy diagrams
\usepackage{tikz}
\usetikzlibrary{matrix, arrows, decorations}
\tikzset{node distance=2.5em, row sep=2.2em, column sep=2.7em, auto}
% simple diagrams
\usepackage[all,cmtip]{xy}
\usepackage{graphicx}
\graphicspath{ {./images/} }
\usepackage{caption}
\usepackage{subcaption}
% for the fib arrow
\usepackage{amssymb}
% mathbb for lowercase bbs
\usepackage{dsfont}
% Some basic objects
\newcommand{\N}{\mathbb{N}} % natural numbers
\newcommand{\Np}{{\mathbb{N}^{>0}}} % positive numbers
\newcommand{\Z}{\mathbb{Z}} % integers
\newcommand{\R}{\mathbb{R}} % reals
\DeclareRobustCommand{\Q}{\mathbb{Q}} % rationals
\renewcommand{\k}{\mathds{k}} % default ground ring
% Basic category stuff
\newcommand{\cat}[1]{\mathbf{#1}} % the category of ...
\newcommand{\opCat}[1]{{#1}^{\text{op}}}% opposite category
\newcommand{\Hom}{\mathbf{Hom}}
\newcommand{\id}{\mathbf{id}}
\newcommand{\Ho}{\cat{Ho}}
% Categories
\newcommand{\Set}{\cat{Set}} % sets
\newcommand{\Top}{\cat{Top}} % topological spaces
\newcommand{\Grp}{\cat{Grp}} % groups
\newcommand{\Ab}{\cat{Ab}} % abelian groups
\newcommand{\DELTA}{\boldsymbol{\Delta}}% the simplicial cat
\newcommand{\simplicial}[1]{\cat{s{#1}}}% simplicial objects
\newcommand{\sSet}{\simplicial{\Set}} % simplicial sets
\newcommand{\Mod}[1]{\cat{{#1}Mod}} % modules over a ring
\newcommand{\Alg}[1]{\cat{{#1}Alg}} % algebras over a ring
\newcommand{\grMod}[1]{\cat{gr\mbox{-}{#1}Mod}} % graded modules over a ring
\newcommand{\grAlg}[1]{\cat{gr\mbox{-}{#1}Alg}} % graded algebras over a ring
\newcommand{\dgMod}[1]{\cat{dg\mbox{-}{#1}Mod}} % differential graded modules over a ring
\newcommand{\dgAlg}[1]{\cat{dg\mbox{-}{#1}Alg}} % differential graded algebras over a ring
\newcommand{\Ch}[1]{\cat{Ch_{n\geq0}({#1})}} % chain complexes
\newcommand{\CoCh}[1]{\cat{Ch^{n\geq0}({#1})}} % cochain complexes
\DeclareRobustCommand{\DGA}{\cat{DGA}} % cochain algebras
\DeclareRobustCommand{\CDGA}{\cat{CDGA}} % commutative cochain algebras
\DeclareRobustCommand{\AugCDGA}{\cat{CDGA^\ast}}% augmentedcommutative cochain algebras
\newcommand{\cof}{\hookrightarrow} % cofibration
\newcommand{\fib}{\twoheadrightarrow} % fibration
\newcommand{\we}{\tot{\simeq}} % weak equivalence
% for use in xy diagrams
\newcommand{\arcof}{\ar@{^{(}->}}
\newcommand{\artcof}{\ar@{^{(}->}|\simeq}
\newcommand{\arfib}{\ar@{->>}}
\newcommand{\artfib}{\ar@{->>}|\simeq}
\newcommand{\arwe}{\ar|-\simeq}
\newcommand{\ariso}{\ar|-\iso}
% adjunction symbol for xymatrices
\newcommand{\xyadj}{\raisebox{0.2\height}{\scalebox{0.5}{$\perp$}}}
% pushout and pullback for xymatrices (makes empty arrow with text)
\newcommand{\xypo}{\ar@{}[dr]|(.75){\scalebox{1.2}{$\ulcorner$}}}
\newcommand{\xypb}{\ar@{}[dr]|(.25){\scalebox{1.2}{$\lrcorner$}}}
%\newcommand{\leftadj}{\ooalign{\hss\rightleftarrows\hss\cr\bot}}
\newcommand{\leftadj}{\rightleftarrows}
% Notation and operators
\newcommand{\I}{\,\mid\,} % seperator in set notation
\newcommand{\del}{\partial} % boundary
\newcommand{\iso}{\cong} % isomorphic
\newcommand{\eq}{\sim} % homotopic
\newcommand{\tot}[1]{\xrightarrow{\,\,{#1}\,\,}} % arrow with name
\newcommand{\toti}[1]{\xleftarrow{\,\,{#1}\,\,}} % left arrow with name
\newcommand{\mapstot}[1]{\xmapsto{\,\,{#1}\,\,}} % mapsto with name
\newcommand{\unit}{\eta}
\newcommand{\counit}{\epsilon}
\DeclareMathOperator*{\im}{im}
\DeclareMathOperator*{\coker}{coker}
\DeclareMathOperator*{\colim}{colim}
\DeclareMathOperator*{\Tor}{Tor}
\DeclareMathOperator*{\Ext}{Ext}
\DeclareMathOperator*{\tensor}{\otimes}
\DeclareMathOperator*{\bigtensor}{\bigotimes}
\renewcommand{\deg}[1]{{|{#1}|}}
\newcommand{\Char}[1]{char({#1})}
\newcommand{\RH}{\widetilde{H}} % reduced homology
\DeclareRobustCommand{\C}{\mathcal{C}} % Serre mod C class
\newcommand{\Apl}[0]{{A_{PL}}} % Apl simplicial set of polynomials
\newcommand{\titleCDGA}{\texorpdfstring{$\CDGA$}{CDGA}}
% restriction of a function
\newcommand\restr[2]{{% we make the whole thing an ordinary symbol
\left.\kern-\nulldelimiterspace % automatically resize the bar with \right
#1 % the function
\vphantom{\big|} % pretend it's a little taller at normal size
\right|_{#2} % this is the delimiter
}}
% Todos in the margin
\newcommand{\todo}[1]{
\addcontentsline{tdo}{todo}{\protect{#1}}
$\ast$ \marginpar{\tiny $\ast$ #1}
}
% Big todos in text
\newcommand{\TODO}[1]{
\addcontentsline{tdo}{todo}{\protect{#1}}
{\tiny $\ast$ #1}
}
% TODO item, as itemize does not work
\newcommand{\titem}[0]{\\-\qquad}
% List of todos
\makeatletter
\newcommand \listoftodos{\section*{Todo list} \@starttoc{tdo}}
\newcommand\l@todo[2]{
\par\noindent \textit{#2}, \parbox{10cm}{#1}\par
}
\makeatother
\theoremstyle{plain}
\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{remark}[theorem]{Remark}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{example}[theorem]{Example}
\newcommand{\EnvTemp}[4]{
\begin{#1}\label{#2:#3}
{#4}
\end{#1}
}
\newcommand{\RefTemp}[3]{{#1}~\ref{#2:#3}}
\newcommand{\Theorem}{\EnvTemp{theorem}{thm}}
\newcommand{\Proposition}{\EnvTemp{proposition}{prop}}
\newcommand{\Lemma}{\EnvTemp{lemma}{lem}}
\newcommand{\Corollary}{\EnvTemp{corollary}{cor}}
\newcommand{\Claim}{\EnvTemp{claim}{clm}}
\newcommand{\Remark}{\EnvTemp{remark}{rmk}}
\newcommand{\Proof}[1]{\begin{proof}{#1}\end{proof}}
\newcommand{\Def}{\emph}
\newcommand{\Definition}{\EnvTemp{definition}{def}}
\newcommand{\Notation}{\EnvTemp{notation}{not}}
\newcommand{\Example}{\EnvTemp{example}{eg}}
\newcommand{\TheoremRef}{\RefTemp{Theorem}{thm}}
\newcommand{\LemmaRef}{\RefTemp{Lemma}{lem}}
\newcommand{\CorollaryRef}{\RefTemp{Corollary}{cor}}
\newcommand{\DefinitionRef}{\RefTemp{Definition}{def}}
% headings for a table
\newcommand*{\thead}[1]{\multicolumn{1}{c}{\bfseries #1}}
% simple way to center an image
\newcommand{\cimage}[2][]{
\begin{center}
\includegraphics[#1]{#2}
\end{center}
}
% simple way to center a diagram
\newcommand{\cdiagrambase}[1]{
\begin{displaymath}
\input{#1}
\end{displaymath}
}
\newcommand{\cdiagram}[1]{
\cdiagrambase{diagrams/#1}
}