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

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

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@ -89,10 +89,12 @@ interest.
With this definition we can also recover reflexivity. That is, for any $A \tp With this definition we can also recover reflexivity. That is, for any $A \tp
\MCU$ and $a \tp A$: \MCU$ and $a \tp A$:
% %
\begin{align} \begin{equation}
\begin{aligned}
\refl & \tp \Path (\lambda i \to A)\ a\ a \\ \refl & \tp \Path (\lambda i \to A)\ a\ a \\
\refl & \defeq \lambda i \to 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 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 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: types:
% %
\begin{equation} \begin{equation}
\begin{alignat}{2} \begin{aligned}
%% \begin{split}
& \isContr && \tp \MCU \to \MCU \\ & \isContr && \tp \MCU \to \MCU \\
& \isContr\ A && \defeq \sum_{c \tp A} \prod_{a \tp A} a \equiv c & \isContr\ A && \defeq \sum_{c \tp A} \prod_{a \tp A} a \equiv c
\end{alignedat} %% \end{split}
\end{aligned}
\end{equation} \end{equation}
% %
The first component of $\isContr\ A$ is called ``the center of contraction''. 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: The next step in the hierarchy is the set of mere propositions:
% %
\begin{equation} \begin{equation}
\begin{alignat}{2} \begin{aligned}
& \isProp && \tp \MCU \to \MCU \\ & \isProp && \tp \MCU \to \MCU \\
& \isProp\ A && \defeq \prod_{a_0, a_1 \tp A} a_0 \equiv a_1 & \isProp\ A && \defeq \prod_{a_0, a_1 \tp A} a_0 \equiv a_1
\end{alignedat} \end{aligned}
\end{equation} \end{equation}
% %
$\isProp\ A$ can be thought of as the set of true and false propositions. It is $\isProp\ A$ 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: Then comes the set of homotopical sets:
% %
\begin{equation} \begin{equation}
\begin{alignat}{2} \begin{aligned}
& \isSet && \tp \MCU \to \MCU \\ & \isSet && \tp \MCU \to \MCU \\
& \isSet\ A && \defeq \prod_{a_0, a_1 \tp A} \isProp\ (a_0 \equiv a_1) & \isSet\ A && \defeq \prod_{a_0, a_1 \tp A} \isProp\ (a_0 \equiv a_1)
\end{alignedat} \end{aligned}
\end{equation} \end{equation}
% %
At this point it should be noted that the term ``set'' is somewhat conflated; 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: The next step in the hierarchy is, as the reader might've guessed, the type:
% %
\begin{equation} \begin{equation}
\begin{alignat}{2} \begin{aligned}
& \isGroupoid && \tp \MCU \to \MCU \\ & \isGroupoid && \tp \MCU \to \MCU \\
& \isGroupoid\ A && \defeq \prod_{a_0, a_1 \tp A} \isSet\ (a_0 \equiv a_1) & \isGroupoid\ A && \defeq \prod_{a_0, a_1 \tp A} \isSet\ (a_0 \equiv a_1)
\end{alignedat} \end{aligned}
\end{equation} \end{equation}
% %
And so it continues. In fact we can generalize this family of types by indexing And so it continues. In fact we can generalize this family of types by indexing

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

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

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