--- a/text/ncat.tex	Wed May 11 14:20:10 2011 -0700
+++ b/text/ncat.tex	Wed May 11 14:32:13 2011 -0700
@@ -1281,7 +1281,10 @@
 \caption{From manifold with boundary collar to marked ball}\label{blah15}\end{figure}
 
 Define the boundary of a marked $k$-ball $(B, N)$ to be the pair $(\bd B \setmin N, \bd N)$.
-Call such a thing a {marked $k{-}1$-hemisphere}.
+Call such a thing a {\it marked $k{-}1$-hemisphere}.
+(A marked $k{-}1$-hemisphere is, of course, just a $k{-}1$-ball with its entire boundary marked.
+We call it a hemisphere instead of a ball because it plays a role analogous
+to the $k{-}1$-spheres in the $n$-category definition.)
 
 \begin{lem}
 \label{lem:hemispheres}