
diff -r 6088d0b8611b -r 3f0f4f4ad048 pnas/pnas.tex
--- a/pnas/pnas.tex	Tue Nov 30 11:30:33 2010 -0800
+++ b/pnas/pnas.tex	Tue Nov 30 11:33:26 2010 -0800
@@ -295,7 +295,7 @@
 {\it strictly associative} composition $\Omega_r\times \Omega_s\to \Omega_{r+s}$.
 Thus we can have the simplicity of strict associativity in exchange for more morphisms.
 We wish to imitate this strategy in higher categories.
-Because we are mainly interested in the case of strong duality, we replace the intervals $[0,r]$ not with
+Because we are mainly interested in the case of pivotal $n$-categories, we replace the intervals $[0,r]$ not with
 a product of $k$ intervals (c.f. \cite{ulrike-tillmann-2008,0909.2212}) but rather with any $k$-ball, that is, 
 any $k$-manifold which is homeomorphic
 to the standard $k$-ball $B^k$.
@@ -316,7 +316,7 @@
 
 Note that the functoriality in the above axiom allows us to operate via
 homeomorphisms which are not the identity on the boundary of the $k$-ball.
-The action of these homeomorphisms gives the ``strong duality" structure.
+The action of these homeomorphisms gives the pivotal structure.
 For this reason we don't subdivide the boundary of a morphism
 into domain and range in the next axiom --- the duality operations can convert between domain and range.
 
@@ -504,7 +504,7 @@
 
 
 \subsection{Example (string diagrams)} \mbox{}
-Fix a ``traditional" $n$-category $C$ with strong duality (e.g.\ a pivotal 2-category).
+Fix a ``traditional" pivotal $n$-category $C$ (e.g.\ a pivotal 2-category).
 Let $X$ be a $k$-ball and define $\cS_C(X)$ to be the set of $C$ string diagrams drawn on $X$;
 that is, certain cell complexes embedded in $X$, with the codimension-$j$ cells labeled by $j$-morphisms of $C$.
 If $X$ is an $n$-ball, identify two such string diagrams if they evaluate to the same $n$-morphism of $C$.




