
diff -r 73cb0346f53c -r d2409e357801 text/ncat.tex
--- a/text/ncat.tex	Fri Jul 24 22:33:31 2009 +0000
+++ b/text/ncat.tex	Tue Jul 28 00:33:08 2009 +0000
@@ -551,6 +551,20 @@
 \nn{give figure for this, or say more?}
 Then $\cE$ has the structure of an $n{-}1$-category.
 
+All marked $k$-balls are homeomorphic, unless $k = 1$ and our manifolds
+are oriented or Spin (but not unoriented or $\text{Pin}_\pm$).
+In this case ($k=1$ and oriented or Spin), there are two types
+of marked 1-balls, call them left-marked and right-marked,
+and hence there are two types of modules, call them right modules and left modules.
+In all other cases ($k>1$ or unoriented or $\text{Pin}_\pm$),
+there is no left/right module distinction.
+
+\medskip
+
+Next we consider tensor products (or, more generally, self tensor products
+or coends).
+
+
 
 \medskip
 \hrule
@@ -564,15 +578,16 @@
 a separate paper):
 \begin{itemize}
 \item tensor products
-\item blob complex is an example of an $A_\infty$ $n$-category
-\item fundamental $n$-groupoid is an example of an $A_\infty$ $n$-category
 \item traditional $n$-cat defs (e.g. *-1-cat, pivotal 2-cat) imply our def of plain $n$-cat
 \item conversely, our def implies other defs
+\item do same for modules; maybe an appendix on relating topological
+vs traditional defs, $n = 1,2$, $A_\infty$ or not, cats, modules, tensor products
 \item traditional $A_\infty$ 1-cat def implies our def
 \item ... and vice-versa (already done in appendix)
 \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
 \end{itemize}
 
 




