
diff -r 091c36b943e7 -r d163ad9543a5 text/tqftreview.tex
--- a/text/tqftreview.tex	Wed Jun 02 12:52:08 2010 -0700
+++ b/text/tqftreview.tex	Wed Jun 02 17:45:13 2010 -0700
@@ -32,7 +32,7 @@
 \begin{example}
 \label{ex:maps-to-a-space(fields)}
 Fix a target space $T$, and let $\cC(X)$ be the set of continuous maps
-from X to $B$.
+from $X$ to $T$.
 \end{example}
 
 \begin{example}
@@ -184,11 +184,11 @@
 
 \subsection{Systems of fields from $n$-categories}
 \label{sec:example:traditional-n-categories(fields)}
-We now describe in more detail systems of fields coming from sub-cell-complexes labeled
+We now describe in more detail Example \ref{ex:traditional-n-categories(fields)}, systems of fields coming from sub-cell-complexes labeled
 by $n$-category morphisms.
 
 Given an $n$-category $C$ with the right sort of duality
-(e.g. pivotal 2-category, 1-category with duals, star 1-category, disklike $n$-category),
+(e.g. a pivotal 2-category, 1-category with duals, star 1-category, disklike $n$-category),
 we can construct a system of fields as follows.
 Roughly speaking, $\cC(X)$ will the set of all embedded cell complexes in $X$
 with codimension $i$ cells labeled by $i$-morphisms of $C$.
@@ -196,9 +196,7 @@
 
 If $X$ has boundary, we require that the cell decompositions are in general
 position with respect to the boundary --- the boundary intersects each cell
-transversely, so cells meeting the boundary are mere half-cells.
-
-Put another way, the cell decompositions we consider are dual to standard cell
+transversely, so cells meeting the boundary are mere half-cells. Put another way, the cell decompositions we consider are dual to standard cell
 decompositions of $X$.
 
 We will always assume that our $n$-categories have linear $n$-morphisms.
@@ -207,7 +205,7 @@
 an object (0-morphism) of the 1-category $C$.
 A field on a 1-manifold $S$ consists of
 \begin{itemize}
-    \item A cell decomposition of $S$ (equivalently, a finite collection
+    \item a cell decomposition of $S$ (equivalently, a finite collection
 of points in the interior of $S$);
     \item a labeling of each 1-cell (and each half 1-cell adjacent to $\bd S$)
 by an object (0-morphism) of $C$;
@@ -233,7 +231,7 @@
 A field of a 1-manifold is defined as in the $n=1$ case, using the 0- and 1-morphisms of $C$.
 A field on a 2-manifold $Y$ consists of
 \begin{itemize}
-    \item A cell decomposition of $Y$ (equivalently, a graph embedded in $Y$ such
+    \item a cell decomposition of $Y$ (equivalently, a graph embedded in $Y$ such
 that each component of the complement is homeomorphic to a disk);
     \item a labeling of each 2-cell (and each partial 2-cell adjacent to $\bd Y$)
 by a 0-morphism of $C$;




