adding cites for pivotal categories, explaining what we mean by *-1-cats. Referee report is now completely finished.
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--- a/text/intro.tex Fri Nov 18 13:17:36 2011 -0800
+++ b/text/intro.tex Fri Nov 18 14:24:17 2011 -0800
@@ -542,7 +542,7 @@
the tongue as well as ``disk-like''.)
Another thing we need a name for is the ability to rotate morphisms around in various ways.
-For 2-categories, ``strict pivotal" is a standard term for what we mean.
+For 2-categories, ``strict pivotal" is a standard term for what we mean. (See \cite{MR1686423, 0908.3347}, although note there the definition is only for monoidal categories; one can think of a monoidal category as a 2-category with only one $0$-morphism, then relax this requirement, to obtain the sensible notion of pivotal (or strict pivotal) for 2-categories. Compare also \cite{1009.0186} which addresses this issue explicitly.)
A more general term is ``duality", but duality comes in various flavors and degrees.
We are mainly interested in a very strong version of duality, where the available ways of
rotating $k$-morphisms correspond to all the ways of rotating $k$-balls.
--- a/text/tqftreview.tex Fri Nov 18 13:17:36 2011 -0800
+++ b/text/tqftreview.tex Fri Nov 18 14:24:17 2011 -0800
@@ -264,8 +264,10 @@
systems of fields coming from embedded cell complexes labeled
by $n$-category morphisms.
-Given an $n$-category $C$ with the right sort of duality
-(e.g. a pivotal 2-category, *-1-category),
+Given an $n$-category $C$ with the right sort of duality,
+e.g., a *-1-category (that is, a 1-category with an involution of the morphisms
+reversing source and target) or a pivotal 2-category,
+(\cite{MR1686423, 0908.3347,1009.0186}),
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 $C$.