Commit 791a5d8b authored by Leonard Guetta's avatar Leonard Guetta
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edited typos

parent f983ae79
......@@ -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
......
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