
diff -r 4d2dad357a49 -r c9f41c18a96f text/ncat.tex
--- 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}
 
 




