--- a/text/ncat.tex	Fri Jul 23 08:14:27 2010 -0600
+++ b/text/ncat.tex	Fri Jul 23 13:52:30 2010 -0700
@@ -946,12 +946,12 @@
 Roughly, a permissible decomposition is like a ball decomposition where we don't care in which order the balls
 are glued up to yield $W$, so long as there is some (non-pathological) way to glue them.
 
-Given permissible decompositions $x = \{X_a\}$ and $y = \{Y_b\}$ or $W$, we say that $x$ is a refinement
+Given permissible decompositions $x = \{X_a\}$ and $y = \{Y_b\}$ of $W$, we say that $x$ is a refinement
 of $y$, or write $x \le y$, if there is a ball decomposition $\du_a X_a = M_0\to\cdots\to M_m = W$
 with $\du_b Y_b = M_i$ for some $i$.
 
 \begin{defn}
-The category (poset) $\cell(W)$ has objects the permissible decompositions of $W$, 
+The poset $\cell(W)$ has objects the permissible decompositions of $W$, 
 and a unique morphism from $x$ to $y$ if and only if $x$ is a refinement of $y$.
 See Figure \ref{partofJfig} for an example.
 \end{defn}