main.tex

% THIS IS NOT THE FILE YOU SHOULD PROCESS. IT IS THE "MAIN" FILE,
% BUT IT GETS INCLUDED BY ONE OF THE hott-xxx.tex FILES. THOSE ARE
% THE MAIN ONES.

% DOCUMENT CLASS
\documentclass[\OPTfontsize]{book}

\PassOptionsToPackage{table}{xcolor}

\usepackage{etex} % We're running out of registers and dimensions, or some such

% PAGE GEOMETRY
\usepackage[papersize={\OPTpagesize},
            twoside,
            includehead,
            top=\OPTtopmargin,
            bottom=\OPTbottommargin,
            inner=\OPTinnermargin,
            outer=\OPToutermargin,
            bindingoffset=\OPTbindingoffset]{geometry}

% HYPERLINKING AND PDF METADATA
\usepackage[backref=page,
            colorlinks,
            citecolor=linkcolor,
            linkcolor=linkcolor,
            urlcolor=linkcolor,
            unicode,
            pdfauthor={Univalent Foundations Program},
            pdftitle={Homotopy Type Theory: Univalent Foundations of Mathematics},
            pdfsubject={Mathematics},
            pdfkeywords={type theory, homotopy theory, univalence axiom}]{hyperref}
\renewcommand{\backref}[1]{}
\renewcommand{\backrefalt}[4]{%
   \ifcase #1 %
   (No citations.)
   \or
   (Cited on page\ #2.)
   \else
   (Cited on pages\ #2.)
   \fi}

% OTHER PACKAGES

% Use this package and stick \layout somewhere in the text to see
% page margins, text size and width etc. Useful for debugging page format.
\usepackage{layout}

%%% Because Germans have umlauts and Slavs have even stranger ways of mangling letters
\usepackage[utf8]{inputenc}

%%% For table {tab:theorems}
\usepackage{pifont}

%%% Multi-Columns for long lists of names
\usepackage{multicol}

%%% Set the fonts
\usepackage{mathpazo}
\usepackage[scaled=0.95]{helvet}
\usepackage{courier}
\linespread{1.05} % Palatino looks better with this

\usepackage{ifpdf}

\usepackage{graphicx}
\DeclareGraphicsExtensions{.png}
\input{bmpsize-hack} % for bounding boxes in dvi mode
\usepackage{comment}

\usepackage{fancyhdr} % To set headers and footers

\usepackage{nextpage} % So we can jump to odd-numbered pages

\usepackage{amssymb,amsmath,amsthm,stmaryrd,mathrsfs,wasysym}
\usepackage{enumitem,mathtools,xspace}
\usepackage{xstring} % For generating singluars and plurals in \backref

\usepackage{xcolor} % For colored cells in tables we need \cellcolor
\usepackage{wallpaper} % For the background image on the cover page

\usepackage{booktabs} % For nice tables
\usepackage{array} % For nice tables

\definecolor{linkcolor}{rgb}{\OPTlinkcolor}
\usepackage{aliascnt}
\usepackage[capitalize]{cleveref}
\usepackage[all,2cell,cmtip]{xy}
\UseAllTwocells
\usepackage{braket} % used for \setof{ ... } macro

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing,arrows}

\usepackage{etoolbox}           % hacking commands for TOC

\usepackage{mathpartir}         % for formal.tex appendix, section 3

\usepackage[numbered]{bookmark} % add chapter/section numbers to the toc in the pdf metadata

\input{macros}

%%%% Indexing
\usepackage{makeidx}
\makeindex

%%%% Header and footers
\pagestyle{fancyplain}
\setlength{\headheight}{15pt}
\renewcommand{\chaptermark}[1]{\markboth{\textsc{Chapter \thechapter. #1}}{}}
\renewcommand{\sectionmark}[1]{\markright{\textsc{\thesection\ #1}}}

\lhead[\fancyplain{}{{\thepage}}]%
      {\fancyplain{}{\nouppercase{\rightmark}}}
\rhead[\fancyplain{}{\nouppercase{\leftmark}}]%
      {\fancyplain{}{\thepage}}
\cfoot[]{}
\lfoot[]{}
\rfoot[]{}

%%%% Chapter & part style
\usepackage[raggedright]{titlesec}
\titleformat{\part}[display]{\fontsize{\OPTpartfont}{\OPTpartfont}\fontseries{m}\fontshape{sc}\selectfont}{\hfil\partname\ \Roman{part}}{\OPTpartskip}{\fontsize{\OPTparttitlefont}{\OPTparttitlefont}\fontseries{b}\fontshape{sc}\selectfont\hfil}
\titleformat{\chapter}[display]{\fontsize{\OPTchapterfont}{\OPTchapterfont}\fontseries{m}\fontshape{it}\selectfont}{\chaptertitlename\ \thechapter}{\OPTchapterskip}{\fontsize{\OPTchaptertitlefont}{\OPTchaptertitlefont}\fontseries{b}\fontshape{n}\selectfont}

% Patch bug in titlesec 2.10.1
\makeatletter
\@ifpackagelater{titlesec}{2016/03/21}{%
 % Package titlesec is on version 2.10.2 or higher, nothing to do
}{\@ifpackagelater{titlesec}{2016/03/15}{%
  % Package titlesec on version 2.10.1, patch accordingly
  \usepackage{etoolbox}%
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  \patchcmd{\ttlh@hang}{\noindent}{}{}{}%
 }{% Package titlesec is on version 2.10.0 or lower, nothing to do %
}}
\makeatother

% To avoid compiling stuff other than what you're working on right
% now, uncomment the following command and give your file as its
% argument.
%\includeonly{}

% For some reason \pagecolor overlays the cover image,
% unless we use it once before the document starts.
\definecolor{covercolor}{cmyk}{\OPTcovercolor}
\definecolor{covertext}{cmyk}{\OPTcovertextcolor}
\pagecolor{white}
\ifpdf
\nopagecolor
\fi

% Make a new page for each exercise, if the option is set
\ifdef{\OPTexerciseperpage}
  {
    \BeforeBeginEnvironment{ex}{\newpage}
  }{}

\begin{document}

% NB: This does not actually appear anywhere because we have
% a custom title page.
\title{Homotopy Type Theory: Univalent Foundations of Mathematics}
\author{The Univalent Foundations Program}


\frontmatter % Turn on arabic page numbers and unnumbered chapters

% Half-title, title, copyright page do not have displayed page numbers
\pagestyle{empty}

\include{front} %%% Title page and copyright

\cleartooddpage

% Add Preface to PDF Metadata but not printed TOC
\hypertarget{preface}{}
\bookmark[dest=preface]{Preface}

% Preface and TOC have arabic numbers
\pagestyle{fancyplain}

\include{preface}

\cleartooddpage[\thispagestyle{empty}]

% Add TOC to PDF Metadata but not printed TOC
\hypertarget{toc}{}
\bookmark[dest=toc]{Table of Contents}

\setcounter{tocdepth}{1}        % chapters and sections for the toc
\tableofcontents
\setcounter{tocdepth}{2}        % chapters, sections, and subsections for the
                                % metadata of the pdf
\cleartooddpage[\thispagestyle{empty}]

\mainmatter % Turn on roman page numbers and numbered chapters

% Turn on headers and footers for mainmatter (must appear after \cleartooddpage)
\pagestyle{fancyplain}

\include{introduction}

\part{Foundations}
\label{part:foundations}

\include{preliminaries}

\include{basics}

\include{logic}

\include{equivalences}

\include{induction}

\include{hits}

\include{hlevels}

\cleartooddpage[\thispagestyle{empty}] % Needed for correct TOC
\part{Mathematics}
\label{part:mathematics}

\include{homotopy}

\include{categories}

\include{setmath}

\include{reals}

%%%% Appendix

\cleartooddpage[\thispagestyle{empty}] % Needed for correct TOC
\phantomsection % Needed for correct TOC also
\part*{Appendix}

% We use magic to get the appendix look like Bibliography and Index

\appendix

\renewcommand{\chaptermark}[1]{\markboth{\textsc{Appendix. \thechapter. #1}}{}}
\renewcommand{\sectionmark}[1]{\markright{\textsc{\thesection\ #1}}}

\include{formal}

% Joke
\nocite{Angiuli13}
\nocite{BauerAcceptanceVideo}

%%%% Bibliography
\bibliographystyle{halpha}
\phantomsection % black magic to get TOC to point to correct page
\addcontentsline{toc}{part}{\bibname}
\markboth{}{\textsc{Bibliography}}
{\renewcommand{\markboth}[2]{} % Prevent bibliography from resetting the header to something silly
\OPTbibliographyfont
\bibliography{references}}

\cleartooddpage[\thispagestyle{empty}]

%%%% Index of symbols

\include{symbols}

\cleartooddpage[\thispagestyle{empty}]

%%%%% Index of terms

%% Global cross-references for index
\indexsee{principle}{axiom}
\indexsee{number!real}{real numbers}
\indexsee{abelian group}{group, abelian}
\indexsee{sequence!Cauchy}{Cauchy sequence}
\indexsee{adjunction}{adjoint functor}
\indexsee{higher topos}{$(\infty,1)$-topos}
\indexsee{topos!higher}{$(\infty,1)$-topos}
\indexsee{source!of a function}{domain}
\indexsee{target!of a function}{codomain}
\indexsee{type!truncation of}{truncation}
\indexsee{propositional!truncation}{truncation}
\indexsee{proof-relevant mathematics}{mathematics, proof-relevant}
\indexsee{classical!mathematics}{mathematics, classical}
\indexsee{classical!logic}{logic}
\indexsee{constructive!mathematics}{mathematics, constructive}
\indexsee{constructive!logic}{logic}
\indexsee{intuitionistic logic}{logic}
\indexsee{definition!inductive}{type, inductive}
\indexsee{inductive!definition}{type, inductive}
\indexsee{bounded!totally}{totally bounded}
\indexsee{sum!of numbers}{addition}
\indexsee{continuous map}{function, continuous}
\indexsee{function!continuity of@``continuity'' of}{``continuity''}
\indexsee{function!functoriality of@``functoriality'' of}{``functoriality''}
\indexsee{codes}{encode-decode method}
\indexsee{inequality}{order}
\indexsee{Coq@\Coq}{proof assistant}
\indexsee{Agda@\Agda}{proof assistant}
\indexsee{NuPRL@\NuPRL}{proof assistant}
\indexsee{generator!of an inductive type}{constructor}
\indexsee{groupoid!.infinity-@$\infty$-}{$\infty$-groupoid}
\indexsee{higher groupoid}{$\infty$-groupoid}
\indexsee{hierarchy!of n-types@of $n$-types}{$n$-type}
\indexsee{homotopy!n-type@$n$-type}{$n$-type}
\indexsee{homotopy!theory, classical}{classical homotopy theory}
\indexsee{homotopy!fiber}{fiber}
\indexsee{homotopy!limit}{limit of types}
\indexsee{homotopy!colimit}{colimit of types}
\indexsee{implementation}{proof assistant}
\indexsee{notation, abuse of}{abuse of notation}
\indexsee{language, abuse of}{abuse of language}
\indexsee{operator!induction}{induction principle}
\indexsee{operator!modal}{modality}
\indexsee{commutative!group}{group, abelian}
\indexsee{countable axiom of choice}{axiom of choice, countable}

% tell the index to get itself into the table of contents
\phantomsection % black magic to get TOC to point to correct page
\addcontentsline{toc}{part}{Index}
\markboth{}{\textsc{Index}}
\renewcommand{\markboth}[2]{}
{\OPTindexfont
\setlength{\columnsep}{\OPTindexcolumnsep}
\printindex}

% The back cover
\include{back}

\end{document}

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