# HG changeset patch # User Scott Morrison # Date 1321655057 28800 # Node ID e8d2f9e0118bff0e8ce9540ca8e423bd59d8440d # Parent b334cb9383ac24b10929a2547c849a3083a9c60e adding cites for pivotal categories, explaining what we mean by *-1-cats. Referee report is now completely finished. diff -r b334cb9383ac -r e8d2f9e0118b RefereeReport.pdf Binary file RefereeReport.pdf has changed diff -r b334cb9383ac -r e8d2f9e0118b text/intro.tex --- 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. diff -r b334cb9383ac -r e8d2f9e0118b text/tqftreview.tex --- 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 $C$.