Use darkorange for all bordercolors

This commit is contained in:
Frederik Hanghøj Iversen 2018-05-15 17:11:01 +02:00
parent 21363dbb78
commit 8a0ea9f4a5
2 changed files with 26 additions and 19 deletions

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@ -8,6 +8,7 @@ This implementation formalizes the following concepts:
\begin{tabular}{ l l } \begin{tabular}{ l l }
Name & Link \\ Name & Link \\
\hline \hline
Equivalences & \sourcelink{Cat.Equivalence} \\
Categories & \sourcelink{Cat.Category} \\ Categories & \sourcelink{Cat.Category} \\
Functors & \sourcelink{Cat.Category.Functor} \\ Functors & \sourcelink{Cat.Category.Functor} \\
Products & \sourcelink{Cat.Category.Product} \\ Products & \sourcelink{Cat.Category.Product} \\
@ -19,12 +20,9 @@ Monads & \sourcelink{Cat.Category.Monad} \\
Kleisli Monads & \sourcelink{Cat.Category.Monad.Kleisli} \\ Kleisli Monads & \sourcelink{Cat.Category.Monad.Kleisli} \\
Monoidal Monads & \sourcelink{Cat.Category.Monad.Monoidal} \\ Monoidal Monads & \sourcelink{Cat.Category.Monad.Monoidal} \\
Voevodsky's construction & \sourcelink{Cat.Category.Monad.Voevodsky} \\ Voevodsky's construction & \sourcelink{Cat.Category.Monad.Voevodsky} \\
%% Categories & \null \\
%%
Opposite category & \sourcelink{Cat.Categories.Opposite} \\ Opposite category & \sourcelink{Cat.Categories.Opposite} \\
Category of sets & \sourcelink{Cat.Categories.Sets} \\ Category of sets & \sourcelink{Cat.Categories.Sets} \\
Span category & \sourcelink{Cat.Categories.Span} \\ Span category & \sourcelink{Cat.Categories.Span} \\
%%
\end{tabular} \end{tabular}
\end{center} \end{center}
% %
@ -42,12 +40,16 @@ Monoids & \sourcelink{Cat.Category.Monoid} \\
\end{tabular} \end{tabular}
\end{center} \end{center}
% %
As well as a range of various results about these. E.g. I have shown that the As well as a range of various results about these. E.g. I have shown
category of sets has products. In the following I aim to demonstrate some of the that the category of sets has products. In the following I aim to
techniques employed in this formalization and in the interest of brevity I will demonstrate some of the techniques employed in this formalization and
not detail all the things I have formalized. In stead, I have selected a parts in the interest of brevity I will not detail all the things I have
of this formalization that highlight some interesting proof techniques relevant formalized. In stead, I have selected parts of this formalization that
to doing proofs in Cubical Agda. highlight some interesting proof techniques relevant to doing proofs
in Cubical Agda. This chapter will focus on the definition of
\emph{categories}, \emph{equivalences}, the \emph{opposite category},
the \emph{category of sets}, \emph{products}, the \emph{span category}
and the two formulations of \emph{monads}.
One such technique that is pervasive to this formalization is the idea of One such technique that is pervasive to this formalization is the idea of
distinguishing types with more or less homotopical structure. To do this I have distinguishing types with more or less homotopical structure. To do this I have
@ -792,16 +794,19 @@ proposition and then use $\lemPropF$. So we prove the generalization:
But $\var{AreInverses}\ f\ g$ is a pair of equations on arrows, so we use But $\var{AreInverses}\ f\ g$ is a pair of equations on arrows, so we use
$\propSig$ and the fact that both $A$ and $B$ are sets to close this proof. $\propSig$ and the fact that both $A$ and $B$ are sets to close this proof.
\subsection{Category of categories} %% \subsection{Category of categories}
Note that this category does in fact not exist. In stead I provide the
definition of the ``raw'' category as well as some of the laws.
Furthermore I provide some helpful lemmas about this raw category. For instance %% Note that this category does in fact not exist. In stead I provide
I have shown what would be the exponential object in such a category. %% the definition of the ``raw'' category as well as some of the laws.
These lemmas can be used to provide the actual exponential object in a context %% Furthermore I provide some helpful lemmas about this raw category.
where we have a witness to this being a category. This is useful if this library %% For instance I have shown what would be the exponential object in
is later extended to talk about higher categories. %% such a category.
%% These lemmas can be used to provide the actual exponential object
%% in a context where we have a witness to this being a category. This
%% is useful if this library is later extended to talk about higher
%% categories.
\section{Products} \section{Products}
\label{sec:products} \label{sec:products}

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@ -3,13 +3,15 @@
\usepackage{natbib} \usepackage{natbib}
\bibliographystyle{plain} \bibliographystyle{plain}
\usepackage{xcolor}
\usepackage[ \usepackage[
hidelinks, %% hidelinks,
pdfusetitle, pdfusetitle,
pdfsubject={category theory}, pdfsubject={category theory},
pdfkeywords={type theory, homotopy theory, category theory, agda}] pdfkeywords={type theory, homotopy theory, category theory, agda}]
{hyperref} {hyperref}
\definecolor{darkorange}{HTML}{ff8c00}
\hypersetup{allbordercolors={darkorange}}
\usepackage{graphicx} \usepackage{graphicx}
\usepackage{parskip} \usepackage{parskip}