diff -r 78db9976b145 -r 09eebcd9dce2 pnas/pnas.tex --- a/pnas/pnas.tex Sat Nov 13 13:23:22 2010 -0800 +++ b/pnas/pnas.tex Sat Nov 13 13:26:29 2010 -0800 @@ -538,8 +538,8 @@ When $\cC$ is the topological $n$-category based on string diagrams for a traditional $n$-category $C$, one can show \nn{cite us} that the above two constructions of the homotopy colimit -are equivalent to the more concrete construction which we describe next, and which we denote $\bc_*(W; C)$. -Roughly speaking, the generators of $\bc_k(W; C)$ are string diagrams on $W$ together with +are equivalent to the more concrete construction which we describe next, and which we denote $\bc_*(W; \cC)$. +Roughly speaking, the generators of $\bc_k(W; \cC)$ are string diagrams on $W$ together with a configuration of $k$ balls (or ``blobs") in $W$ whose interiors are pairwise disjoint or nested. The restriction of the string diagram to innermost blobs is required to be ``null" in the sense that it evaluates to a zero $n$-morphism of $C$. @@ -552,7 +552,7 @@ The $k$-blob group $\bc_k(W; \cC)$ is generated by the $k$-blob diagrams. A $k$-blob diagram consists of \begin{itemize} \item a permissible collection of $k$ embedded balls, -\item an ordering of the balls, and +\item an ordering of the balls, and \nn{what about reordering?} \item for each resulting piece of $W$, a field, \end{itemize} such that for any innermost blob $B$, the field on $B$ goes to zero under the gluing map from $\cC$. We call such a field a `null field on $B$'.