Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Leonard Guetta
memoire
Commits
fbd37cb9
Commit
fbd37cb9
authored
Oct 20, 2020
by
Leonard Guetta
Browse files
First complete version of the thesis !
parent
d70ea50d
Changes
4
Expand all
Hide whitespace changes
Inline
Side-by-side
2cat.tex
View file @
fbd37cb9
\chapter
{
Homotopy and homology type of free
$
2
$
-categories
}
\section
{
Preliminaries: the case of free
$
1
$
-categories
}
\section
{
Preliminaries: the case of free
$
1
$
-categories
}
\label
{
section:prelimfreecat
}
In this section, we review some homotopical results on free
(
$
1
$
-)categories that will be of great help in the sequel.
\begin{paragr}
...
...
@@ -737,7 +737,7 @@ In practice, we will use the following corollary.
horizontal weak equivalences. The result follows then from Proposition
\ref
{
prop:bisimplicialcocontinuous
}
.
\end{proof}
\section
{
Bisimplicial nerve for 2-categories
}
\section
{
Bisimplicial nerve for 2-categories
}
\label
{
section:bisimplicialnerve
}
We shall now describe a ``nerve'' for
$
2
$
-categories with values in bisimplicial
sets and recall a few results that shows that this nerve is, in some sense,
equivalent to the nerve defined in
\ref
{
paragr:nerve
}
.
...
...
hmtpy.tex
View file @
fbd37cb9
...
...
@@ -822,7 +822,7 @@ The nerve functor $N_{\omega} : \omega\Cat \to \Psh{\Delta}$ sends equivalences
\end{align*}
\end{paragr}
\begin{proposition}
(Folk Theorem
$
A
$
) Let
\begin{proposition}
\label
{
prop:folkthmA
}
(Folk Theorem
$
A
$
) Let
\[
\begin
{
tikzcd
}
[
column sep
=
small
]
A
\ar
[
rr,"u"
]
\ar
[
dr,"v"'
]
&
&
B
\ar
[
dl,"w"
]
\\
...
...
introduction.tex
View file @
fbd37cb9
This diff is collapsed.
Click to expand it.
main.pdf
View file @
fbd37cb9
No preview for this file type
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment