text/ncat.tex
changeset 858 1fc5fff34251
parent 857 4ad6325c7c7d
child 859 76a569bb2cec
--- 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.