--- a/pnas/pnas.tex	Wed Nov 10 10:40:29 2010 +0900
+++ b/pnas/pnas.tex	Tue Nov 09 17:48:16 2010 -0800
@@ -239,7 +239,7 @@
 For $c\in \cl{\cC}_{k-1}(\bd X)$ we define $\cC_k(X; c) = \bd^{-1}(c)$.
 
 Many of the examples we are interested in are enriched in some auxiliary category $\cS$
-(e.g. vector spaces or rings, or, in the $A_\infty$ case, chain complex or topological spaces).
+(e.g. vector spaces or rings, or, in the $A_\infty$ case, chain complexes or topological spaces).
 This means that in the top dimension $k=n$ the sets $\cC_n(X; c)$ have the structure
 of an object of $\cS$, and all of the structure maps of the category (above and below) are
 compatible with the $\cS$ structure on $\cC_n(X; c)$.