--- a/pnas/pnas.tex	Tue Nov 02 21:22:53 2010 +0900
+++ b/pnas/pnas.tex	Tue Nov 02 06:18:43 2010 -0700
@@ -223,6 +223,10 @@
 homeomorphisms to the category of sets and bijections.
 \end{axiom}
 
+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.
+
 Next we consider domains and ranges of $k$-morphisms.
 Because we assume strong duality, it doesn't make much sense to subdivide the boundary of a morphism
 into domain and range --- the duality operations can convert domain to range and vice-versa.