--- a/text/ncat.tex	Fri May 06 14:22:35 2011 -0700
+++ b/text/ncat.tex	Fri May 06 14:56:13 2011 -0700
@@ -523,6 +523,11 @@
 Product morphisms are compatible with gluing (composition).
 Let $\pi:E\to X$, $\pi_1:E_1\to X_1$, and $\pi_2:E_2\to X_2$ 
 be pinched products with $E = E_1\cup E_2$.
+(See Figure \ref{pinched_prod_unions}.)  
+Note that $X_1$ and $X_2$ can be identified with subsets of $X$, 
+but $X_1 \cap X_2$ might not be codimension 1, and indeed we might have $X_1 = X_2 = X$.
+We assume that there is a decomposition of $X$ into balls which is compatible with
+$X_1$ and $X_2$.
 Let $a\in \cC(X)$, and let $a_i$ denote the restriction of $a$ to $X_i\sub X$.
 Then 
 \[