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 }
Name & Link \\
\hline
Equivalences & \sourcelink{Cat.Equivalence} \\
Categories & \sourcelink{Cat.Category} \\
Functors & \sourcelink{Cat.Category.Functor} \\
Products & \sourcelink{Cat.Category.Product} \\
@ -19,12 +20,9 @@ Monads & \sourcelink{Cat.Category.Monad} \\
Kleisli Monads & \sourcelink{Cat.Category.Monad.Kleisli} \\
Monoidal Monads & \sourcelink{Cat.Category.Monad.Monoidal} \\
Voevodsky's construction & \sourcelink{Cat.Category.Monad.Voevodsky} \\
%% Categories & \null \\
%%
Opposite category & \sourcelink{Cat.Categories.Opposite} \\
Category of sets & \sourcelink{Cat.Categories.Sets} \\
Span category & \sourcelink{Cat.Categories.Span} \\
%%
\end{tabular}
\end{center}
%
@ -42,12 +40,16 @@ Monoids & \sourcelink{Cat.Category.Monoid} \\
\end{tabular}
\end{center}
%
As well as a range of various results about these. E.g. I have shown that the
category of sets has products. In the following I aim to demonstrate some of the
techniques employed in this formalization and in the interest of brevity I will
not detail all the things I have formalized. In stead, I have selected a parts
of this formalization that highlight some interesting proof techniques relevant
to doing proofs in Cubical Agda.
As well as a range of various results about these. E.g. I have shown
that the category of sets has products. In the following I aim to
demonstrate some of the techniques employed in this formalization and
in the interest of brevity I will not detail all the things I have
formalized. In stead, I have selected parts of this formalization that
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
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
$\propSig$ and the fact that both $A$ and $B$ are sets to close this proof.
\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.
%% \subsection{Category of categories}
Furthermore I provide some helpful lemmas about this raw category. For instance
I have shown what would be the exponential object in such a category.
%% 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.
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.
%% Furthermore I provide some helpful lemmas about this raw category.
%% For instance I have shown what would be the exponential object in
%% 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}
\label{sec:products}

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