
diff -r c1cf892a4ab7 -r 6a7f2a6295d1 pnas/pnas.tex
--- a/pnas/pnas.tex	Wed Nov 17 10:56:17 2010 -0800
+++ b/pnas/pnas.tex	Wed Nov 17 11:16:27 2010 -0800
@@ -531,9 +531,12 @@
 
 
 \subsubsection{Colimits}
-\nn{Motivation: How can we extend an $n$-category from balls to arbitrary manifolds?}
+Our definition of an $n$-category is essentially a collection of functors defined on $k$-balls (and homeomorphisms) for $k \leq n$ satisfying certain axioms. It is natural to consider extending such functors to the larger categories of all $k$-manifolds (again, with homeomorphisms). In fact, the axioms stated above explictly require such an extension to $k$-spheres for $k<n$.
+
+The natural construction achieving this is the colimit.
+\nn{continue}
+
 \nn{Mention that the axioms for $n$-categories can be stated in terms of decompositions of balls?}
-\nn{Explain codimension colimits here too}
 
 We can now give a straightforward but rather abstract definition of the blob complex of an $n$-manifold $W$
 with coefficients in the $n$-category $\cC$ as the homotopy colimit along $\cell(W)$




