--- a/text/ncat.tex Wed May 04 14:47:43 2011 -0600
+++ b/text/ncat.tex Fri May 06 14:11:43 2011 -0700
@@ -674,6 +674,12 @@
\medskip
+We define a $j$ times monoidal $n$-category to be an $(n{+}j)$-category $\cC$ where
+$\cC(X)$ is a trivial 1-element set if $X$ is a $k$-ball with $k<j$.
+See Example \ref{ex:bord-cat}.
+
+\medskip
+
The alert reader will have already noticed that our definition of a (ordinary) $n$-category
is extremely similar to our definition of a system of fields.
There are two differences.
@@ -806,20 +812,6 @@
(See \S\ref{sec:constructing-a-tqft}.)
\end{example}
-\noop{
-\nn{shouldn't this go elsewhere? we haven't yet discussed constructing a system of fields from
-an n-cat}
-Recall we described a system of fields and local relations based on a ``traditional $n$-category"
-$C$ in Example \ref{ex:traditional-n-categories(fields)} above.
-\nn{KW: We already refer to \S \ref{sec:fields} above}
-Constructing a system of fields from $\cC$ recovers that example.
-\todo{Except that it doesn't: pasting diagrams v.s. string diagrams.}
-\nn{KW: but the above example is all about string diagrams. the only difference is at the top level,
-where the quotient is built in.
-but (string diagrams)/(relations) is isomorphic to
-(pasting diagrams composed of smaller string diagrams)/(relations)}
-}
-
\begin{example}[The bordism $n$-category of $d$-manifolds, ordinary version]
\label{ex:bord-cat}