Add frontmatter

doc/chalmerstitle.sty

@@ -39,6 +39,47 @@
 \newcommand*{\researchgroup}[1]{\gdef\@researchgroup{#1}}
 \newcommand*{\subtitle}[1]{\gdef\@subtitle{#1}}
 
+%% \begin{titlepage}
+\newgeometry{top=3cm, bottom=3cm,
+	left=2.25 cm, right=2.25cm}	% Temporarily change margins
+% Cover page background 
+%% \AddToShipoutPicture*{\backgroundpic{-4}{56.7}{figure/auxiliary/frontpage_gu_eng.pdf}}
+%% \AddToShipoutPicture*{\backgroundpic{-4}{56.7}{logo_eng.pdf}}
+%% \includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf}
+%% \begin{center}
+%%   \includegraphics[width=0.5\paperwidth,height=\paperheight,keepaspectratio]{logo_eng.pdf}%
+%% \end{center}
+%% \addtolength{\voffset}{2cm}
+
+% Cover picture (replace with your own or delete)
+{\Huge\@title}\\[.5cm]
+{\Large A formalization of category theory in Cubical Agda}\\[2.5cm]
+\begin{center}
+\includegraphics[\linewidth,height=0.35\paperheight,keepaspectratio]{isomorphism.png}
+\end{center}
+
+% Cover text
+\vfill
+%% \renewcommand{\familydefault}{\sfdefault} \normalfont % Set cover page font
+Master's thesis in Computer Science \\[1cm]
+{\Large\@author} \\[2cm]
+\textsc{Department of Computer Science and Engineering}\\
+\textsc{Chalmers University of Technology}\\
+\textsc{University of Gothenburg}\\
+\textsc{Gothenburg, Sweden \the\year}
+
+%% \renewcommand{\familydefault}{\rmdefault} \normalfont % Reset standard font
+%% \end{titlepage}
+
+
+% BACK OF COVER PAGE (BLANK PAGE)
+\newpage
+\newgeometry{a4paper}	% Temporarily change margins
+\restoregeometry
+\thispagestyle{empty}
+\null
+
+
 \renewcommand*{\maketitle}{%
 \begin{titlepage}
 
@@ -56,11 +97,11 @@
 	\includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf}
   \vspace{5mm}
 	
-	Department of Computer Science and Engineering\\
-	\emph{\@researchgroup}\\
+	\textsc{Department of Computer Science and Engineering}\\
+	\textsc{{\@researchgroup}}\\
 	%Name of research group (if applicable)\\
 	\textsc{\@institution} \\
-	Gothenburg, Sweden \the\year \\
+	\textsc{Gothenburg, Sweden \the\year}\\
 \end{center}
 
 
@@ -105,5 +146,5 @@ Telephone +46 31 772 1000 \setlength{\parskip}{0.5cm}\\
 %Printed by [Name of printing company]\\
 Gothenburg, Sweden \the\year
 
-
+\restoregeometry
 \end{titlepage}}

doc/implementation.tex

@@ -149,7 +149,7 @@ $$
 So to give the continuous function $I \to \IsPreCategory$ that is our goal we
 introduce $i \tp I$ and proceed by constructing an element of $\IsPreCategory$
 by using that all the projections are propositions to generate paths between all
-projections. Once we have such a path e.g. $p : \isIdentity_a \equiv
+projections. Once we have such a path e.g. $p \tp \isIdentity_a \equiv
 \isIdentity_b$ we can elimiate it with $i$ and thus obtaining $p\ i \tp
 \isIdentity_{p\ i}$ and this element satisfies exactly that it corresponds to
 the corresponding projections at either endpoint. Thus the element we construct
@@ -198,9 +198,9 @@ provide since, as we have shown, $\IsPreCategory$ is a proposition. However,
 even though $\Univalent$ is also a proposition, we cannot use this directly to
 show the latter. This is becasue $\isProp$ talks about non-dependent paths. To
 `promote' this to a dependent path we can use another useful combinator;
-$\lemPropF$. Given a type $A \tp \MCU$ and a type family on $A$; $B : A \to
+$\lemPropF$. Given a type $A \tp \MCU$ and a type family on $A$; $B \tp A \to
 \MCU$. Let $P$ be a proposition indexed by an element of $A$ and say we have a
-path between some two elements in $A$; $p : a_0 \equiv a_1$ then we can built a
+path between some two elements in $A$; $p \tp a_0 \equiv a_1$ then we can built a
 heterogeneous path between any two $b$'s at the endpoints:
 %
 $$
@@ -240,15 +240,15 @@ here, but the curious reader can check the implementation for the details.
 
 \section{Equivalences}
 \label{sec:equiv}
-The usual notion of a function $f : A \to B$ having an inverses is:
+The usual notion of a function $f \tp A \to B$ having an inverses is:
 %
 $$
-\sum_{g : B \to A} f \comp g \equiv \identity_{B} \x g \comp f \equiv \identity_{A}
+\sum_{g \tp B \to A} f \comp g \equiv \identity_{B} \x g \comp f \equiv \identity_{A}
 $$
 %
 This is defined in \cite[p. 129]{hott-2013} and is referred to as the a
 quasi-inverse. At the same place \cite{hott-2013} gives an ``interface'' for
-what an equivalence $\isEquiv : (A \to B) \to \MCU$ must supply:
+what an equivalence $\isEquiv \tp (A \to B) \to \MCU$ must supply:
 %
 \begin{itemize}
 \item
@@ -264,11 +264,11 @@ how to work with equivalences and 2) to use ad-hoc definitions of equivalences.
 The specific instantiation of $\isEquiv$ as defined in \cite{cubical-agda} is:
 %
 $$
-isEquiv\ f \defeq \prod_{b : B} \isContr\ (\fiber\ f\ b)
+isEquiv\ f \defeq \prod_{b \tp B} \isContr\ (\fiber\ f\ b)
 $$
 where
 $$
-\fiber\ f\ b \defeq \sum_{a \tp A} b \equiv f\ a
+\fiber\ f\ b \defeq \sum_{a \tp A} \left( b \equiv f\ a \right)
 $$
 %
 I give it's definition here mainly for completeness, because as I stated we can
@@ -473,7 +473,7 @@ B$ is simply an arrow $f \tp \mathit{Arrow}\ A\ B$ and it's inverse $g \tp
 \mathit{Arrow}\ B\ A$. In the opposite category $g$ will play the role of the
 isomorphism and $f$ will be the inverse. Similarly we can go in the opposite
 direction. I name these maps $\mathit{shuffle} \tp (A \approxeq B) \to (A
-\approxeq_{\bC} B)$ and $\mathit{shuffle}^{-1} : (A \approxeq_{\bC} B) \to (A
+\approxeq_{\bC} B)$ and $\mathit{shuffle}^{-1} \tp (A \approxeq_{\bC} B) \to (A
 \approxeq B)$ respectively.
 
 As the inverse of $\idToIso_{\mathit{Op}}$ I will pick $\zeta \defeq \eta \comp
@@ -670,7 +670,7 @@ proposition and then use $\lemPropF$. So we prove the generalization:
 %
 \begin{align}
 \label{eq:propAreInversesGen}
-\prod_{g : B \to A} \isProp\ (\mathit{AreInverses}\ f\ g)
+\prod_{g \tp B \to A} \isProp\ (\mathit{AreInverses}\ f\ g)
 \end{align}
 %
 But $\mathit{AreInverses}\ f\ g$ is a pair of equations on arrows, so we use
@@ -716,8 +716,6 @@ that there exists a unique arrow $\pi \tp \Arrow\ X\ (A \x B)$ satisfying
 %% \prod_{X \tp Object} \prod_{f \tp \Arrow\ X\ A} \prod_{g \tp \Arrow\ X\ B}\\
 %% \uexists_{f \x g \tp \Arrow\ X\ (A \x B)}
 \pi_1 \lll \pi \equiv f \x \pi_2 \lll \pi \equiv g
-%% ump : ∀ {X : Object} (f : ℂ [ X , A ]) (g : ℂ [ X , B ])
-%%           → ∃![ f×g ] (ℂ [ fst ∘ f×g ] ≡ f P.× ℂ [ snd ∘ f×g ] ≡ g)
 \end{align}
 %
 $\pi$ is called the product (arrow) of $f$ and $g$.

doc/macros.tex

@@ -5,7 +5,7 @@
                      \hbox{\scriptsize.}\hbox{\scriptsize.}}}%
   =}
 
-\newcommand{\defeq}{\triangleq}
+\newcommand{\defeq}{\mathrel{\triangleq}}
 %% Alternatively:
 %% \newcommand{\defeq}{≔}
 \newcommand{\bN}{\mathbb{N}}
@@ -21,7 +21,7 @@
 \newcommand{\comp}{\circ}
 \newcommand{\x}{\times}
 \newcommand\inv[1]{#1\raisebox{1.15ex}{$\scriptscriptstyle-\!1$}}
-\newcommand{\tp}{\;\mathord{:}\;}
+\newcommand{\tp}{\mathrel{:}}
 \newcommand{\Type}{\mathcal{U}}
 
 \usepackage{graphicx}

doc/main.tex

@@ -4,7 +4,7 @@
 \input{packages.tex}
 \input{macros.tex}
 
-\title{Univalent Categories in Cubical Agda}
+\title{Univalent Categories}
 \author{Frederik Hanghøj Iversen}
 
 %% \usepackage[
@@ -26,7 +26,7 @@
 %%   researchgroup=Programming Logic Group
 %%   ]{chalmerstitle}
 \usepackage{chalmerstitle}
-\subtitle{}
+\subtitle{A formalization of category theory in Cubical Agda}
 \authoremail{hanghj@student.chalmers.se}
 \newcommand{\chalmers}{Chalmers University of Technology}
 \supervisor{Thierry Coquand}

doc/packages.tex

@@ -15,7 +15,7 @@
 \usepackage{amssymb,amsmath,amsthm,stmaryrd,mathrsfs,wasysym}
 \usepackage[toc,page]{appendix}
 \usepackage{xspace}
-%% \usepackage{geometry}
+\usepackage{geometry}
 
 % \setlength{\parskip}{10pt}