--- a/text/ncat.tex Tue Sep 21 07:37:41 2010 -0700
+++ b/text/ncat.tex Tue Sep 21 14:44:17 2010 -0700
@@ -1034,8 +1034,7 @@
is more involved.
We will describe two different (but homotopy equivalent) versions of the homotopy colimit of $\psi_{\cC;W}$.
The first is the usual one, which works for any indexing category.
-The second construction, we we call the {\it local} homotopy colimit,
-\nn{give it a different name?}
+The second construction, which we call the {\it local} homotopy colimit,
is more closely related to the blob complex
construction of \S \ref{sec:blob-definition} and takes advantage of local (gluing) properties
of the indexing category $\cell(W)$.
@@ -1351,7 +1350,7 @@
plain ball case.
Note that a marked pinched product can be decomposed into either
two marked pinched products or a plain pinched product and a marked pinched product.
-\nn{should give figure}
+\nn{should maybe give figure}
\begin{module-axiom}[Product (identity) morphisms]
For each pinched product $\pi:E\to M$, with $M$ a marked $k$-ball and $E$ a marked
@@ -1828,7 +1827,7 @@
where $B^j$ is the standard $j$-ball.
A 1-marked $k$-ball can be decomposed in various ways into smaller balls, which are either
(a) smaller 1-marked $k$-balls, (b) 0-marked $k$-balls, or (c) plain $k$-balls.
-(See Figure \nn{need figure}.)
+(See Figure \nn{need figure, and improve caption on other figure}.)
We now proceed as in the above module definitions.
\begin{figure}[t] \centering
@@ -2190,7 +2189,7 @@
\begin{lem}
Assume $n\ge 2$ and fix $E$ and $E'$ as above.
-The any two sequences of elementary moves connecting $E$ to $E'$
+Then any two sequences of elementary moves connecting $E$ to $E'$
are related by a sequence of the two movie moves defined above.
\end{lem}
@@ -2211,7 +2210,7 @@
rotating the 0-sphere $E$ around the 1-sphere $\bd X$.
But if $n=1$, then we are in the case of ordinary algebroids and bimodules,
and this is just the well-known ``Frobenius reciprocity" result for bimodules.
-\nn{find citation for this. Evans and Kawahigashi?}
+\nn{find citation for this. Evans and Kawahigashi? Bisch!}
\medskip
@@ -2240,7 +2239,7 @@
\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}
+%\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}