qsdf

pres.tex

-\documentclass{beamer}
+\documentclass[handout]{beamer}
 
 %\usepackage[utf8]{inputenc}
 \usepackage{mystyle}
@@ -154,10 +154,10 @@
     \]
     where:
     \begin{itemize}[label=$\bullet$]
-      \item $\Ho(\oo\Cat^{\Th})$ is the localization of $\oo\Cat$ with respect to
+      \item $\Ho(\oo\Cat^{\Th})$ is the localization of $\oo\Cat$ w.r.t
         the Thomason equivalences,
-        \item $\Ho(\Psh{\Delta})$ is the localization of $\Psh{\Delta}$ with
-          respect to weak equivalences of simplicial sets.
+        \item $\Ho(\Psh{\Delta})$ is the localization of $\Psh{\Delta}$ w.r.t
+          the  weak equivalences of simplicial sets.
       \end{itemize}
     % Where $\Ho(-)$ stands for the localized category (or better
     % the localized pre-derivator or even weak $(\oo,1)$\nbd{}category).
@@ -523,7 +523,7 @@
         \pause
         Hence, both $\sH^{\pol}$ and $\sH^{\sing}$ are obtained as left derived
         functors of $\lambda$ but not w.r.t the same class of weak equivalences.
-        \begin{exampleblock}{Corollary}
+        \begin{exampleblock}{Corollary (abstract non-sense)}
           There is a canonical natural transformation
           \[
             \begin{tikzcd}[ampersand replacement=\&]
@@ -544,7 +544,7 @@
             comparison map}.
           \pause
           \begin{block}{Definition}
-            An $\oo$\nbd{}category $C$ is \alert{homogically coherent} if the
+            An $\oo$\nbd{}category $C$ is \alert{homologically coherent} if the
             map
             \[
               \pi_C : \sH^{\sing}(C) \to \sH^{\folk}(C)
@@ -552,7 +552,7 @@
             is an isomorphism.
           \end{block}
           \pause
-          Goal: Understand which $\oo$\nbd{}categories are homogically coherent. 
+          Goal: Understand which $\oo$\nbd{}categories are homologically coherent. 
         \end{frame}
         \begin{frame}
           \frametitle{Polygraphic homology is not homotopical}
@@ -572,7 +572,7 @@
           \pause
           \begin{exampleblock}{New slogan}
             The polygraphic homology is a
-          way of computing the singular homology of homogically coherent
+          way of computing the singular homology of homologically coherent
           $\oo$\nbd{}categories.
           \end{exampleblock}
         \end{frame}
@@ -597,7 +597,7 @@
             for $k=2,3$, for any $\oo$\nbd{}category $C$ ?
           \end{exampleblock}
         \end{frame}
-        \section{Detecting homologically coherent $\oo$-categories I}
+        \section{Detecting homologically coherent $\oo$-categories}
         \begin{frame}\frametitle{Preliminaries: oplax contractile
             $\oo$\nbd{}categories}
           \begin{block}{Definition}
@@ -633,7 +633,7 @@
           In other words, for a diagram $d : I \to \oo\Cat$, the
           canonical map
           \[
-            \hocolim_{I}^{\folk}(d) \to \hocolim_{I}^{\Th}(d)
+            \hocolim_{I}^{\Th}(d) \to \hocolim_{I}^{\folk}(d)
           \]
           is not an isomorphism in general.
           \pause
@@ -710,7 +710,7 @@
                A}^{\folk}A/a\simeq \colim_{a \in A}A/a\simeq A.\]
            \pause
            Let $f : P \longrightarrow A$ be a folk cofibrant
-           resolution of $A$. \pause (Note that $P$ is free but need not be a
+           replacement of $A$. \pause (Note that $P$ is free but need not be a
            $1$\nbd{}category).
            % \pause How do we prove that ? Let us take a detour.
          %   \pause In order to do
@@ -791,7 +791,7 @@
          cofibrant. \hfill CQFD
          \end{itemize}
        \end{frame}
-       \section{Detecting homologically coherent $\oo$-categories II}
+       \section{The case of $2$-categories}
          %   \begin{frame}\frametitle{A criterion}
          %     A variation of the homotopy colimit criterion:
          %         \begin{exampleblock}{Proposition}