Commit 2a65308a by Leonard Guetta

### very very slowly but surely

parent 05c221bd
 ... @@ -499,6 +499,7 @@ ... @@ -499,6 +499,7 @@ \] \] which is natural in $C$. We refer to it as the \alert{canonical which is natural in $C$. We refer to it as the \alert{canonical comparison map}. comparison map}. \pause \begin{block}{Definition} \begin{block}{Definition} An $\oo$\nbd{}category $C$ is \alert{homogically coherent} if the An $\oo$\nbd{}category $C$ is \alert{homogically coherent} if the map map ... @@ -584,13 +585,38 @@ ... @@ -584,13 +585,38 @@ \begin{block}{Proposition} \begin{block}{Proposition} Let $C$ be an $\oo$\nbd{}category. Suppose that there exists $d : I Let$C$be an$\oo$\nbd{}category. Suppose that there exists$d : I \to \oo\Cat$such that: \to \oo\Cat$ such that: % \begin{enumerate}[label=($\roman$)] \begin{enumerate}[label=(\roman*)] % \item $\item<2-> \displaystyle\hocolim^{\pol}_I(d)\simeq \hocolim^{\Th}_I(d) % \hocolim^{\pol}_I(d)\simeq \hocolim^{\Th}_I(d) \simeq C \simeq C, %$ \item<3-> for each $i \in \Ob(I)$, the $\oo$\nbd{}category $d(i)$ is % \end{enumerate} homologically coherent. \end{block} \end{enumerate} \end{frame} \pause\pause Then $C$ is homologically coherent. \end{block} % \pause % Often, we will use: \end{frame} \begin{frame}\frametitle{In practice} \begin{exampleblock}{Corollary} Let $\begin{tikzcd}[ampersand replacement=\&] A \ar[r,"u"] \ar[d,"v"] \& B \ar[d] \\ C \ar[r] \& D \ar[from=1-1,to=2-2,"\ulcorner",phantom] \end{tikzcd}$ be a cocartesian square in $\oo\Cat$. If \begin{itemize}[label=$\bullet$] \item<2-> $A$,$B$ and $C$ are homologically coherent, \item<3-> $u$ or $v$ is a folk cofibration, \item<4-> the square is homotopy cocartesian w.r.t Thomason equivalence, \end{itemize} then $D$ is homologically coherent. \end{exampleblock} \end{frame} \end{document} \end{document} %%% Local Variables: %%% Local Variables: ... ...
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