very very slowly but surely

pres.tex

@@ -499,6 +499,7 @@
           \]
           which is natural in $C$. We refer to it as the \alert{canonical
             comparison map}.
+          \pause
           \begin{block}{Definition}
             An $\oo$\nbd{}category $C$ is \alert{homogically coherent} if the
             map
@@ -584,13 +585,38 @@
               \begin{block}{Proposition}
            Let $C$ be an $\oo$\nbd{}category. Suppose that there exists $d : I
            \to \oo\Cat$ such that:
-           % \begin{enumerate}[label=($\roman$)]
-           % \item \[
-           %     \hocolim^{\pol}_I(d)\simeq \hocolim^{\Th}_I(d) \simeq C
-           %   \]
-           %   \end{enumerate}
-          \end{block}
-          \end{frame}
+           \begin{enumerate}[label=(\roman*)]
+           \item<2-> $\displaystyle\hocolim^{\pol}_I(d)\simeq \hocolim^{\Th}_I(d)
+             \simeq C,$
+             \item<3-> for each $i \in \Ob(I)$, the $\oo$\nbd{}category $d(i)$ is
+               homologically coherent.
+             \end{enumerate}
+             \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}
  
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