text/hochschild.tex
changeset 321 76c301fdf0a2
parent 314 6e23226d1cca
child 342 1d76e832d32f
--- a/text/hochschild.tex	Wed Jun 02 08:43:12 2010 -0700
+++ b/text/hochschild.tex	Wed Jun 02 11:45:19 2010 -0700
@@ -7,8 +7,7 @@
 greater than zero.
 In this section we analyze the blob complex in dimension $n=1$.
 We find that $\bc_*(S^1, \cC)$ is homotopy equivalent to the 
-Hochschild complex of the 1-category $\cC$.
-\nn{cat vs fields --- need to make sure this is clear}
+Hochschild complex of the 1-category $\cC$. (Recall from \S \ref{sec:example:traditional-n-categories(fields)} that a $1$-category gives rise to a $1$-dimensional system of fields; as usual, talking about the blob complex with coefficients in a $n$-category means first passing to the corresponding $n$ dimensional system of fields.)
 Thus the blob complex is a natural generalization of something already
 known to be interesting in higher homological degrees.