--- a/text/ncat.tex	Fri May 06 15:00:46 2011 -0700
+++ b/text/ncat.tex	Fri May 06 15:23:26 2011 -0700
@@ -397,8 +397,12 @@
 $$
 \caption{Examples of pinched products}\label{pinched_prods}
 \end{figure}
-(The need for a strengthened version will become apparent in Appendix \ref{sec:comparing-defs}
-where we construct a traditional category from a disk-like category.)
+The need for a strengthened version will become apparent in Appendix \ref{sec:comparing-defs}
+where we construct a traditional category from a disk-like category.
+For example, ``half-pinched" products of 1-balls are used to construct weak identities for 1-morphisms
+in 2-categories.
+We also need fully-pinched products to define collar maps below (see Figure \ref{glue-collar}).
+
 Define a {\it pinched product} to be a map
 \[
 	\pi: E\to X