# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1304716303 25200
# Node ID 4b1f08238baefbb8785eaa34b06b9c73122cc0a8
# Parent  0c1255ac996a92badb960c537abbacee219f7a71
added brief def of monoidal n-cats; killed some old invisible comments

diff -r 0c1255ac996a -r 4b1f08238bae text/ncat.tex
--- 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}