--- a/text/ncat.tex Thu Aug 11 12:50:50 2011 -0700
+++ b/text/ncat.tex Thu Aug 11 13:23:33 2011 -0700
@@ -1171,8 +1171,8 @@
\label{ex:blob-complexes-of-balls}
Fix an $n{-}k$-dimensional manifold $F$ and an $n$-dimensional system of fields $\cE$.
We will define an $A_\infty$ disk-like $k$-category $\cC$.
-When $X$ is a $m$-ball, with $m<k$, define $\cC(X) = \cE(X\times F)$.
-When $X$ is an $k$-ball,
+When $X$ is an $m$-ball, with $m<k$, define $\cC(X) = \cE(X\times F)$.
+When $X$ is a $k$-ball,
define $\cC(X; c) = \bc^\cE_*(X\times F; c)$
where $\bc^\cE_*$ denotes the blob complex based on $\cE$.
\end{example}
@@ -1283,7 +1283,7 @@
system of fields and local relations, followed by the usual TQFT definition of a
vector space invariant of manifolds given as Definition \ref{defn:TQFT-invariant}.
For an $A_\infty$ disk-like $n$-category, $\cl{\cC}$ is defined using a homotopy colimit instead.
-Recall that we can take a ordinary disk-like $n$-category $\cC$ and pass to the ``free resolution",
+Recall that we can take an ordinary disk-like $n$-category $\cC$ and pass to the ``free resolution",
an $A_\infty$ disk-like $n$-category $\bc_*(\cC)$, by computing the blob complex of balls
(recall Example \ref{ex:blob-complexes-of-balls} above).
We will show in Corollary \ref{cor:new-old} below that the homotopy colimit invariant