
diff -r 8ed3aeb78778 -r 4a23163843a9 text/ncat.tex
--- a/text/ncat.tex	Fri Jul 30 18:36:08 2010 -0400
+++ b/text/ncat.tex	Fri Jul 30 20:19:17 2010 -0400
@@ -871,7 +871,6 @@
 \begin{example}[$E_n$ algebras]
 \rm
 \label{ex:e-n-alg}
-
 Let $A$ be an $\cE\cB_n$-algebra.
 Note that this implies a $\Diff(B^n)$ action on $A$, 
 since $\cE\cB_n$ contains a copy of $\Diff(B^n)$.
@@ -892,14 +891,13 @@
 also comes from the $\cE\cB_n$ action on $A$.
 \nn{should we spell this out?}
 
-\nn{Should remark that the associated hocolim for manifolds
-agrees with Lurie's topological chiral homology construction; maybe wait
-until next subsection to say that?}
-
 Conversely, one can show that a topological $A_\infty$ $n$-category $\cC$, where the $k$-morphisms
 $\cC(X)$ are trivial (single point) for $k<n$, gives rise to 
 an $\cE\cB_n$-algebra.
 \nn{The paper is already long; is it worth giving details here?}
+
+If we apply the homotopy colimit construction of the next subsection to this example, 
+we get an instance of Lurie's topological chiral homology construction.
 \end{example}
 
 
@@ -2355,20 +2353,17 @@
 In particular, if $F: X\to X$ is the identity on $\bd X$ then $f$ acts trivially, as required by
 Axiom \ref{axiom:extended-isotopies} of \S\ref{ss:n-cat-def}.
 
-
-\nn{still to do: gluing, associativity, collar maps}
+We define product $n{+}1$-morphisms to be identity maps of modules.
 
-\medskip
-\hrule
-\medskip
-
+To define (binary) composition of $n{+}1$-morphisms, choose the obvious common equator
+then compose the module maps.
 
 
-Stuff that remains to be done (either below or in an appendix or in a separate section or in
-a separate paper):
-\begin{itemize}
-\item discuss Morita equivalence
-\item functors
-\end{itemize}
+\nn{still to do: associativity}
+
+\medskip
+
+\nn{Stuff that remains to be done (either below or in an appendix or in a separate section or in
+a separate paper): discuss Morita equivalence; functors}
 
 




