
diff -r 1cfa95e6b8bb -r 6b6c565bd76e pnas/pnas.tex
--- a/pnas/pnas.tex	Tue Nov 23 09:28:45 2010 -0800
+++ b/pnas/pnas.tex	Wed Nov 24 09:51:28 2010 -0700
@@ -237,15 +237,6 @@
 yields a higher categorical and higher dimensional generalization of Deligne's
 conjecture on Hochschild cochains and the little 2-disks operad.
 
-\nn{needs revision}
-Of course, there are currently many interesting alternative notions of $n$-category and of TQFT.
-We note that our $n$-categories are both more and less general
-than the ``fully dualizable" ones which play a prominent role in \cite{0905.0465}.
-They are more general in that we make no duality assumptions in the top dimension $n{+}1$.
-They are less general in that we impose stronger duality requirements in dimensions 0 through $n$.
-Thus our $n$-categories correspond to $(n{+}\epsilon)$-dimensional {\it unoriented} or {\it oriented} TQFTs, while
-Lurie's (fully dualizable) $n$-categories correspond to $(n{+}1)$-dimensional {\it framed} TQFTs.
-
 At several points we only sketch an argument briefly; full details can be found in \cite{1009.5025}. 
 In this paper we attempt to give a clear view of the big picture without getting 
 bogged down in technical details.
@@ -272,6 +263,14 @@
 %We separate these two tasks, and address only the first, which becomes much easier when not burdened by the second.
 %More specifically, life is easier when working with maximal, rather than minimal, collections of axioms.}
 
+Of course, there are currently many interesting alternative notions of $n$-category.
+We note that our $n$-categories are both more and less general
+than the ``fully dualizable" ones which play a prominent role in \cite{0905.0465}.
+They are more general in that we make no duality assumptions in the top dimension $n{+}1$.
+They are less general in that we impose stronger duality requirements in dimensions 0 through $n$.
+Thus our $n$-categories correspond to $(n{+}\epsilon)$-dimensional {\it unoriented} or {\it oriented} TQFTs, while
+Lurie's (fully dualizable) $n$-categories correspond to $(n{+}1)$-dimensional {\it framed} TQFTs.
+
 We will define two variations simultaneously,  as all but one of the axioms are identical in the two cases.
 These variations are ``plain $n$-categories", where homeomorphisms fixing the boundary
 act trivially on the sets associated to $n$-balls




