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}