--- a/text/tqftreview.tex Fri Jun 04 11:42:07 2010 -0700
+++ b/text/tqftreview.tex Fri Jun 04 17:00:18 2010 -0700
@@ -48,9 +48,9 @@
\begin{example}
\label{ex:traditional-n-categories(fields)}
Fix an $n$-category $C$, and let $\cC(X)$ be
-the set of sub-cell-complexes of $X$ with codimension-$j$ cells labeled by
+the set of embedded cell complexes in $X$ with codimension-$j$ cells labeled by
$j$-morphisms of $C$.
-One can think of such sub-cell-complexes as dual to pasting diagrams for $C$.
+One can think of such embedded cell complexes as dual to pasting diagrams for $C$.
This is described in more detail in \S \ref{sec:example:traditional-n-categories(fields)}.
\end{example}
@@ -199,7 +199,7 @@
\subsection{Systems of fields from $n$-categories}
\label{sec:example:traditional-n-categories(fields)}
We now describe in more detail Example \ref{ex:traditional-n-categories(fields)},
-systems of fields coming from sub-cell-complexes labeled
+systems of fields coming from embedded cell complexes labeled
by $n$-category morphisms.
Given an $n$-category $C$ with the right sort of duality
@@ -308,12 +308,12 @@
homeomorphic to the standard $n$-ball and all $c \in \cC(\bd B)$,
satisfying the following properties.
\begin{enumerate}
-\item functoriality:
+\item Functoriality:
$f(U(B; c)) = U(B', f(c))$ for all homeomorphisms $f: B \to B'$
-\item local relations imply extended isotopy:
+\item Local relations imply extended isotopy:
if $x, y \in \cC(B; c)$ and $x$ is extended isotopic
to $y$, then $x-y \in U(B; c)$.
-\item ideal with respect to gluing:
+\item Ideal with respect to gluing:
if $B = B' \cup B''$, $x\in U(B')$, and $c\in \cC(B'')$, then $x\bullet r \in U(B)$
\end{enumerate}
\end{defn}