Merge branch 'dev'

This commit is contained in:
Frederik Hanghøj Iversen 2018-05-31 01:07:31 +02:00
commit 33f7e2ebbb
11 changed files with 44 additions and 28 deletions

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@ -4,8 +4,10 @@ build: src/**.agda
clean: clean:
find src -name "*.agdai" -type f -delete find src -name "*.agdai" -type f -delete
html: html: src/**.agda
agda --html src/Cat.agda agda --html src/Cat.agda
upload: html upload: html
scp -r html/ remote11.chalmers.se:www/cat/doc/ scp -r html/ remote11.chalmers.se:www/cat/doc/
.PHONY: upload clean

1
doc/.gitignore vendored
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@ -4,6 +4,7 @@
*.log *.log
*.out *.out
*.pdf *.pdf
!assets/**
*.bbl *.bbl
*.blg *.blg
*.toc *.toc

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@ -1,3 +1,13 @@
Presentation
====
Find one clear goal.
Remember crowd-control.
Leave out:
lemPropF
Talk about structure of library: Talk about structure of library:
=== ===

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@ -1 +0,0 @@
\chapter*{Acknowledgements}

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@ -7,7 +7,7 @@ can conjure up various proofs. I also want to recognize the support
of Knud Højgaards Fond who graciously sponsored me with a 20.000 DKK of Knud Højgaards Fond who graciously sponsored me with a 20.000 DKK
scholarship which helped toward sponsoring the two years I have spent scholarship which helped toward sponsoring the two years I have spent
studying abroad. I would also like to give a warm thanks to my fellow studying abroad. I would also like to give a warm thanks to my fellow
students Pierre Kraft and Nachiappan Villiappan who have made the time students Pierre~Kraft and Nachiappan~Valliappan who have made the time
spent working on the thesis way more enjoyable. Lastly I would like to spent working on the thesis way more enjoyable. Lastly I would like to
give a special thanks to Valentina Méndez who have been a great moral give a special thanks to Valentina~Méndez who have been a great moral
support throughout the whole process. support throughout the whole process.

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doc/assets/logo_eng.pdf Normal file

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@ -80,7 +80,7 @@ Master's thesis in Computer Science
\vfill \vfill
\centering \centering
\includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf} \includegraphics[width=0.2\pdfpagewidth]{assets/logo_eng.pdf}
\vspace{5mm} \vspace{5mm}
\textsc{Department of Computer Science and Engineering}\\ \textsc{Department of Computer Science and Engineering}\\

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@ -75,8 +75,8 @@ some limitations inherent in ITT and -- by extension -- Agda.
Consider the functions: Consider the functions:
% %
\begin{align*}% \begin{align*}%
\var{zeroLeft} & \defeq \lambda\; (n \tp \bN) \to (0 + n \tp \bN) \\ \var{zeroLeft} & \defeq λ\; (n \tp \bN) \to (0 + n \tp \bN) \\
\var{zeroRight} & \defeq \lambda\; (n \tp \bN) \to (n + 0 \tp \bN) \var{zeroRight} & \defeq λ\; (n \tp \bN) \to (n + 0 \tp \bN)
\end{align*}% \end{align*}%
% %
The term $n + 0$ is \nomenindex{definitionally} equal to $n$, which we The term $n + 0$ is \nomenindex{definitionally} equal to $n$, which we

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@ -4,8 +4,12 @@
%% \usecolortheme[named=seagull]{structure} %% \usecolortheme[named=seagull]{structure}
\input{packages.tex} \input{packages.tex}
\input{macros.tex} \input{macros.tex}
\title[Univalent Categories]{Univalent Categories\\ \footnotesize A formalization of category theory in Cubical Agda}
\title{Univalent Categories}
\subtitle{A formalization of category theory in Cubical Agda}
\newcommand{\myname}{Frederik Hangh{\o}j Iversen} \newcommand{\myname}{Frederik Hangh{\o}j Iversen}
\author[\myname]{ \author[\myname]{
\myname\\ \myname\\
@ -74,14 +78,14 @@
\framesubtitle{Definition} \framesubtitle{Definition}
Heterogeneous paths Heterogeneous paths
\begin{equation*} \begin{equation*}
\Path \tp (P \tp I → \MCU) → P\ 0 → P\ 1 → \MCU \Path \tp (P \tp \I\MCU) → P\ 0 → P\ 1 → \MCU
\end{equation*} \end{equation*}
\pause \pause
For $P \tp I → \MCU$, $A \tp \MCU$ and $a_0, a_1 \tp A$ For $P \tp \I\MCU$, $A \tp \MCU$ and $a_0, a_1 \tp A$
inhabitants of $\Path\ P\ a_0\ a_1$ are like functions inhabitants of $\Path\ P\ a_0\ a_1$ are like functions
% %
$$ $$
p \tp_{i \tp I} P\ i p \tp_{i \tp \I} P\ i
$$ $$
% %
Which satisfy $p\ 0 & = a_0$ and $p\ 1 & = a_1$ Which satisfy $p\ 0 & = a_0$ and $p\ 1 & = a_1$
@ -255,13 +259,13 @@
\end{align*} \end{align*}
where where
$$ $$
\phi\ f ≜ \identity \phi\ f ≜
( \lll f ≡ f ) ( \identity \lll f ≡ f )
× ×
( f \lll \identity ≡ f) ( f \lll \identity ≡ f)
$$ $$
\pause \pause
Let $\approxeq$ denote ismorphism of objects. We can then construct Let $\approxeq$ denote isomorphism of objects. We can then construct
the identity isomorphism in any category: the identity isomorphism in any category:
$$ $$
\identity , \identity , \var{isIdentity} \tp A \approxeq A \identity , \identity , \var{isIdentity} \tp A \approxeq A

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@ -37,7 +37,7 @@ Master's thesis in Computer Science
\vfill \vfill
\centering \centering
\includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf} \includegraphics[width=0.2\pdfpagewidth]{assets/logo_eng.pdf}
\vspace{5mm} \vspace{5mm}
\textsc{Department of Computer Science and Engineering}\\ \textsc{Department of Computer Science and Engineering}\\