Merge branch 'dev'
This commit is contained in:
commit
33f7e2ebbb
4
Makefile
4
Makefile
|
@ -4,8 +4,10 @@ build: src/**.agda
|
|||
clean:
|
||||
find src -name "*.agdai" -type f -delete
|
||||
|
||||
html:
|
||||
html: src/**.agda
|
||||
agda --html src/Cat.agda
|
||||
|
||||
upload: html
|
||||
scp -r html/ remote11.chalmers.se:www/cat/doc/
|
||||
|
||||
.PHONY: upload clean
|
||||
|
|
1
doc/.gitignore
vendored
1
doc/.gitignore
vendored
|
@ -4,6 +4,7 @@
|
|||
*.log
|
||||
*.out
|
||||
*.pdf
|
||||
!assets/**
|
||||
*.bbl
|
||||
*.blg
|
||||
*.toc
|
||||
|
|
|
@ -1,3 +1,13 @@
|
|||
Presentation
|
||||
====
|
||||
Find one clear goal.
|
||||
|
||||
Remember crowd-control.
|
||||
|
||||
Leave out:
|
||||
lemPropF
|
||||
|
||||
|
||||
Talk about structure of library:
|
||||
===
|
||||
|
||||
|
|
|
@ -1 +0,0 @@
|
|||
\chapter*{Acknowledgements}
|
|
@ -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
|
||||
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
|
||||
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
|
||||
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.
|
||||
|
|
BIN
doc/assets/logo_eng.pdf
Normal file
BIN
doc/assets/logo_eng.pdf
Normal file
Binary file not shown.
|
@ -80,7 +80,7 @@ Master's thesis in Computer Science
|
|||
|
||||
\vfill
|
||||
\centering
|
||||
\includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf}
|
||||
\includegraphics[width=0.2\pdfpagewidth]{assets/logo_eng.pdf}
|
||||
\vspace{5mm}
|
||||
|
||||
\textsc{Department of Computer Science and Engineering}\\
|
||||
|
|
|
@ -75,8 +75,8 @@ some limitations inherent in ITT and -- by extension -- Agda.
|
|||
Consider the functions:
|
||||
%
|
||||
\begin{align*}%
|
||||
\var{zeroLeft} & \defeq \lambda\; (n \tp \bN) \to (0 + n \tp \bN) \\
|
||||
\var{zeroRight} & \defeq \lambda\; (n \tp \bN) \to (n + 0 \tp \bN)
|
||||
\var{zeroLeft} & \defeq λ\; (n \tp \bN) \to (0 + n \tp \bN) \\
|
||||
\var{zeroRight} & \defeq λ\; (n \tp \bN) \to (n + 0 \tp \bN)
|
||||
\end{align*}%
|
||||
%
|
||||
The term $n + 0$ is \nomenindex{definitionally} equal to $n$, which we
|
||||
|
|
|
@ -4,8 +4,12 @@
|
|||
%% \usecolortheme[named=seagull]{structure}
|
||||
|
||||
\input{packages.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}
|
||||
\author[\myname]{
|
||||
\myname\\
|
||||
|
@ -74,14 +78,14 @@
|
|||
\framesubtitle{Definition}
|
||||
Heterogeneous paths
|
||||
\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*}
|
||||
\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
|
||||
%
|
||||
$$
|
||||
p \tp ∏_{i \tp I} P\ i
|
||||
p \tp ∏_{i \tp \I} P\ i
|
||||
$$
|
||||
%
|
||||
Which satisfy $p\ 0 & = a_0$ and $p\ 1 & = a_1$
|
||||
|
@ -255,13 +259,13 @@
|
|||
\end{align*}
|
||||
where
|
||||
$$
|
||||
\phi\ f ≜ \identity
|
||||
( \lll f ≡ f )
|
||||
\phi\ f ≜
|
||||
( \identity \lll f ≡ f )
|
||||
×
|
||||
( f \lll \identity ≡ f)
|
||||
$$
|
||||
\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:
|
||||
$$
|
||||
\identity , \identity , \var{isIdentity} \tp A \approxeq A
|
||||
|
|
|
@ -37,7 +37,7 @@ Master's thesis in Computer Science
|
|||
|
||||
\vfill
|
||||
\centering
|
||||
\includegraphics[width=0.2\pdfpagewidth]{logo_eng.pdf}
|
||||
\includegraphics[width=0.2\pdfpagewidth]{assets/logo_eng.pdf}
|
||||
\vspace{5mm}
|
||||
|
||||
\textsc{Department of Computer Science and Engineering}\\
|
||||
|
|
Loading…
Reference in a new issue