Remove tex warnings

This commit is contained in:
Frederik Hanghøj Iversen 2018-05-08 02:00:23 +02:00
parent 7faf0961c5
commit e18730e0e5
5 changed files with 23 additions and 20 deletions

View file

@ -38,12 +38,11 @@
\newcommand*{\department}[1]{\gdef\@department{#1}}
\newcommand*{\researchgroup}[1]{\gdef\@researchgroup{#1}}
\newcommand*{\subtitle}[1]{\gdef\@subtitle{#1}}
%% FRONTMATTER
\newcommand*{\myfrontmatter}{%
\newgeometry{top=3cm, bottom=3cm,left=2.25 cm, right=2.25cm}
\begingroup
\thispagestyle{empty}
\usepackage{noto}
\fontseries{sb}
%% \fontfamily{noto}\selectfont
{\Huge\@title}\\[.5cm]
{\Large A formalization of category theory in Cubical Agda}\\[2.5cm]
\begin{center}
@ -55,17 +54,16 @@
{\Large\@author}\\[.5cm]
Master's thesis in Computer Science
\endgroup
%% \renewcommand{\familydefault}{\rmdefault} \normalfont % Reset standard font
%% \end{titlepage}
% BACK OF COVER PAGE (BLANK PAGE)
\newpage
\newgeometry{a4paper} % Temporarily change margins
\restoregeometry
%% \newgeometry{a4paper} % Temporarily change margins
%% \restoregeometry
\thispagestyle{empty}
\null
}
\renewcommand*{\maketitle}{%
\begin{titlepage}

View file

@ -89,10 +89,12 @@ interest.
With this definition we can also recover reflexivity. That is, for any $A \tp
\MCU$ and $a \tp A$:
%
\begin{align}
\begin{equation}
\begin{aligned}
\refl & \tp \Path (\lambda i \to A)\ a\ a \\
\refl & \defeq \lambda i \to a
\end{align}
\end{aligned}
\end{equation}
%
Or, in other terms; reflexivity is the path in $A$ that is $a$ at the left
endpoint as well as at the right endpoint. It is inhabited by the path which
@ -113,10 +115,12 @@ structure''. At the bottom of this hierarchy we have the set of contractible
types:
%
\begin{equation}
\begin{alignat}{2}
\begin{aligned}
%% \begin{split}
& \isContr && \tp \MCU \to \MCU \\
& \isContr\ A && \defeq \sum_{c \tp A} \prod_{a \tp A} a \equiv c
\end{alignedat}
%% \end{split}
\end{aligned}
\end{equation}
%
The first component of $\isContr\ A$ is called ``the center of contraction''.
@ -127,10 +131,10 @@ contractible, then it is isomorphic to the unit-type $\top$.
The next step in the hierarchy is the set of mere propositions:
%
\begin{equation}
\begin{alignat}{2}
\begin{aligned}
& \isProp && \tp \MCU \to \MCU \\
& \isProp\ A && \defeq \prod_{a_0, a_1 \tp A} a_0 \equiv a_1
\end{alignedat}
\end{aligned}
\end{equation}
%
$\isProp\ A$ can be thought of as the set of true and false propositions. It is
@ -144,10 +148,10 @@ stress that we have $\isProp\ A$.
Then comes the set of homotopical sets:
%
\begin{equation}
\begin{alignat}{2}
\begin{aligned}
& \isSet && \tp \MCU \to \MCU \\
& \isSet\ A && \defeq \prod_{a_0, a_1 \tp A} \isProp\ (a_0 \equiv a_1)
\end{alignedat}
\end{aligned}
\end{equation}
%
At this point it should be noted that the term ``set'' is somewhat conflated;
@ -158,10 +162,10 @@ if $\isSet\ A$ is inhabited.
The next step in the hierarchy is, as the reader might've guessed, the type:
%
\begin{equation}
\begin{alignat}{2}
\begin{aligned}
& \isGroupoid && \tp \MCU \to \MCU \\
& \isGroupoid\ A && \defeq \prod_{a_0, a_1 \tp A} \isSet\ (a_0 \equiv a_1)
\end{alignedat}
\end{aligned}
\end{equation}
%
And so it continues. In fact we can generalize this family of types by indexing

View file

@ -195,7 +195,7 @@ Name & Agda & Notation \\
\nomen{Type} & \texttt{Set} & $\Type$ \\
\nomen{Set} & \texttt{Σ Set IsSet} & $\Set$ \\
Function, morphism, map & \texttt{A → B} & $A → B$ \\
Dependent- ditto & \texttt{(a : A) → B} & $_{a \tp A} B$ \\
Dependent- ditto & \texttt{(a : A) → B} & $_{a \tp A} B$ \\
\nomen{Arrow} & \texttt{Arrow A B} & $\Arrow\ A\ B$ \\
\nomen{Object} & \texttt{C.Object} & $̱ℂ.Object$ \\
Definition & \texttt{=} & $̱\defeq$ \\

View file

@ -25,6 +25,7 @@
%% department=Department of Computer Science and Engineering,
%% researchgroup=Programming Logic Group
%% ]{chalmerstitle}
\usepackage{chalmerstitle}
\subtitle{A formalization of category theory in Cubical Agda}
\authoremail{hanghj@student.chalmers.se}
@ -48,7 +49,7 @@
\newcommand*{\rom}[1]{\expandafter\@slowroman\romannumeral #1@}
\makeatother
\begin{document}
\myfrontmatter
\pagenumbering{roman}
\maketitle
\addtocontents{toc}{\protect\thispagestyle{empty}}

View file

@ -45,7 +45,7 @@
%% \setmonofont{FreeMono.otf}
\pagestyle{fancyplain}
%% \pagestyle{fancyplain}
\setlength{\headheight}{15pt}
\renewcommand{\chaptermark}[1]{\markboth{\textsc{Chapter \thechapter. #1}}{}}
\renewcommand{\sectionmark}[1]{\markright{\textsc{\thesection\ #1}}}