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Leonard Guetta
memoire
Commits
791a5d8b
Commit
791a5d8b
authored
Oct 21, 2020
by
Leonard Guetta
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edited typos
parent
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introduction.tex
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791a5d8b
...
...
@@ -93,7 +93,8 @@ for the category of (strict) $\oo$\nbd{}categories.
\text
{
Do we have
}
H
_
k
^{
\pol
}
(C)
\simeq
H
_
k
^{
\sing
}
(C)
\text
{
for any
}
\oo\text
{
-category
}
C
\text
{
?
}
\end{equation}
\fi
A partial answer to this question is given by Lafont and Métayer in
\cite
{
lafont2009polygraphic
}
: for a monoid
$
M
$
(seen as category and hence as
\cite
{
lafont2009polygraphic
}
: for a monoid
$
M
$
(seen as category with one
object and hence as
an
$
\oo
$
\nbd
{}
category), we have
$
H
_{
\bullet
}^{
\pol
}
(
M
)
\simeq
H
_{
\bullet
}^{
\sing
}
(
M
)
$
. In fact, the original motivation for polygraphic
homology was the homology of monoids and is part of a program that generalizes
...
...
@@ -463,7 +464,7 @@ for the category of (strict) $\oo$\nbd{}categories.
$
\oo
$
\nbd
{}
category is
\good
{}
(Proposition
\ref
{
prop:contractibleisgood
}
).
Finally, the sixth and last chapter of the thesis revolves around the homology
of free
$
2
$
\nbd
{}
categories. The goal pursued is to try
and
understand which
of free
$
2
$
\nbd
{}
categories. The goal pursued is to try
to
understand which
free
$
2
$
\nbd
{}
categories are
\good
{}
. In order to do so, we give a criterion
to detect homotopy cocartesian square with respect to Thomason equivalences
(Proposition
\ref
{
prop:critverthorThomhmtpysquare
}
) based on the homotopy
...
...
main.pdf
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omegacat.tex
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