
diff -r 3f180943709f -r b62214646c4f text/ncat.tex
--- a/text/ncat.tex	Wed Aug 26 01:21:59 2009 +0000
+++ b/text/ncat.tex	Wed Aug 26 02:35:24 2009 +0000
@@ -457,7 +457,8 @@
 $\psi_\cC(x)\to \cC(W)$, these maps are compatible with the refinement maps
 above, and $\cC(W)$ is universal with respect to these properties.
 In the $A_\infty$ case, it means 
-\nn{.... need to check if there is a def in the literature before writing this down}
+\nn{.... need to check if there is a def in the literature before writing this down;
+homotopy colimit I think}
 
 More concretely, in the plain case enriched over vector spaces, and with $\dim(W) = n$, we can take
 \[
@@ -469,6 +470,7 @@
 
 In the $A_\infty$ case enriched over chain complexes, the concrete description of the colimit
 is as follows.
+\nn{should probably rewrite this to be compatible with some standard reference}
 Define an $m$-sequence to be a sequence $x_0 \le x_1 \le \dots \le x_m$ of permissible decompositions.
 Such sequences (for all $m$) form a simplicial set.
 Let
@@ -815,6 +817,12 @@
 
 
 
+\subsection{The $n{+}1$-category of sphere modules}
+
+Outline:
+\begin{itemize}
+\item 
+\end{itemize}
 
 
 
@@ -838,7 +846,9 @@
 \item say something about unoriented vs oriented vs spin vs pin for $n=1$ (and $n=2$?)
 \item spell out what difference (if any) Top vs PL vs Smooth makes
 \item explain relation between old-fashioned blob homology and new-fangled blob homology
-\item define $n{+}1$-cat of $n$-cats; discuss Morita equivalence
+(follows as special case of product formula (product with a point).
+\item define $n{+}1$-cat of $n$-cats (a.k.a.\ $n{+}1$-category of generalized bimodules
+a.k.a.\ $n{+}1$-category of sphere modules); discuss Morita equivalence
 \end{itemize}
 
 




