diff -r 4ad6325c7c7d -r 1fc5fff34251 text/ncat.tex --- a/text/ncat.tex Wed Aug 03 08:13:17 2011 -0700 +++ b/text/ncat.tex Fri Aug 05 12:02:42 2011 -0600 @@ -2147,7 +2147,7 @@ \medskip -Our first task is to define an $n$-category $m$-sphere modules, for $0\le m \le n-1$. +Our first task is to define an $n$-category $m$-sphere module, for $0\le m \le n-1$. These will be defined in terms of certain classes of marked balls, very similarly to the definition of $n$-category modules above. (This, in turn, is very similar to our definition of $n$-category.) @@ -2392,7 +2392,7 @@ duality assumptions on the lower morphisms. These are required because we define the spaces of $n{+}1$-morphisms by making arbitrary choices of incoming and outgoing boundaries for each $n$-ball. -The additional duality assumptions are needed to prove independence of our definition form these choices. +The additional duality assumptions are needed to prove independence of our definition from these choices. Let $X$ be an $n{+}1$-ball, and let $c$ be a decoration of its boundary by a cell complex labeled by 0- through $n$-morphisms, as above.