\usepackage[utf8]{inputenc}

\usepackage{natbib}
\bibliographystyle{plain}

\usepackage{xcolor}
%% \mode<report>{
\usepackage[
  %% hidelinks,
  pdfusetitle,
  pdfsubject={category theory},
  pdfkeywords={type theory, homotopy theory, category theory, agda}]
  {hyperref}
%% }
%% \definecolor{darkorange}{HTML}{ff8c00}
%% \hypersetup{allbordercolors={darkorange}}
\hypersetup{hidelinks}
\usepackage{graphicx}
%% \usepackage[active,tightpage]{preview}

\usepackage{parskip}
\usepackage{multicol}
\usepackage{amssymb,amsmath,amsthm,stmaryrd,mathrsfs,wasysym}
\usepackage[toc,page]{appendix}
\usepackage{xspace}
\usepackage[paper=a4paper,top=3cm,bottom=3cm]{geometry}
\usepackage{makeidx}
\makeindex
% \setlength{\parskip}{10pt}

% \usepackage{tikz}
% \usetikzlibrary{arrows, decorations.markings}

% \usepackage{chngcntr}
% \counterwithout{figure}{section}
\numberwithin{equation}{section}

\usepackage{listings}
\usepackage{fancyvrb}

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

\usepackage{lmodern}

\usepackage{enumerate}
\usepackage{verbatim}

\usepackage{fontspec}
\usepackage[light]{sourcecodepro}
%% \setmonofont{Latin Modern Mono}
%% \setmonofont[Mapping=tex-text]{FreeMono.otf}
%% \setmonofont{FreeMono.otf}


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

% Allows for the use of unicode-letters:
\usepackage{unicode-math}

%% \RequirePackage{kvoptions}

\usepackage{pgffor}
\lstset
  {basicstyle=\ttfamily
  ,columns=fullflexible
  ,breaklines=true
  ,inputencoding=utf8
  ,extendedchars=true
  %% ,literate={á}{{\'a}}1 {ã}{{\~a}}1 {é}{{\'e}}1
  }
  
\usepackage{newunicodechar}

%% \setmainfont{PT Serif}
\newfontfamily{\fallbackfont}{FreeMono.otf}[Scale=MatchLowercase]
%% \setmonofont[Mapping=tex-text]{FreeMono.otf}
\DeclareTextFontCommand{\textfallback}{\fallbackfont}
\newunicodechar{∨}{\textfallback{∨}}
\newunicodechar{∧}{\textfallback{∧}}
\newunicodechar{⊔}{\textfallback{⊔}}
%% \newunicodechar{≊}{\textfallback{≊}}
\newunicodechar{∈}{\textfallback{∈}}
\newunicodechar{ℂ}{\textfallback{ℂ}}
\newunicodechar{∘}{\textfallback{∘}}
\newunicodechar{⟨}{\textfallback{⟨}}
\newunicodechar{⟩}{\textfallback{⟩}}
\newunicodechar{∎}{\textfallback{∎}}
%% \newunicodechar{𝒜}{\textfallback{𝒜}}
%% \newunicodechar{ℬ}{\textfallback{ℬ}}
%% \newunicodechar{≊}{\textfallback{≊}}
\makeatletter
\newcommand*{\rom}[1]{\expandafter\@slowroman\romannumeral #1@}
\makeatother
\makeatletter

\newcommand\frontmatter{%
    \cleardoublepage
  %\@mainmatterfalse
  \pagenumbering{roman}}

\newcommand\mainmatter{%
    \cleardoublepage
 % \@mainmattertrue
  \pagenumbering{arabic}}

\newcommand\backmatter{%
  \if@openright
    \cleardoublepage
  \else
    \clearpage
  \fi
 % \@mainmatterfalse
   }

\makeatother
\usepackage{xspace}
\usepackage{tikz}
\newcommand{\ExternalLink}{%
    \tikz[x=1.2ex, y=1.2ex, baseline=-0.05ex]{% 
        \begin{scope}[x=1ex, y=1ex]
            \clip (-0.1,-0.1) 
                --++ (-0, 1.2) 
                --++ (0.6, 0) 
                --++ (0, -0.6) 
                --++ (0.6, 0) 
                --++ (0, -1);
            \path[draw, 
                line width = 0.5, 
                rounded corners=0.5] 
                (0,0) rectangle (1,1);
        \end{scope}
        \path[draw, line width = 0.5] (0.5, 0.5) 
            -- (1, 1);
        \path[draw, line width = 0.5] (0.6, 1) 
            -- (1, 1) -- (1, 0.6);
        }
    }
\usepackage{ dsfont }

\usepackage{eso-pic}
\newcommand{\backgroundpic}[3]{
	\put(#1,#2){
	\parbox[b][\paperheight]{\paperwidth}{
	\centering
	\includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio]{#3}}}}