diff -r cd2ebc293e6b -r 42ca1dee3441 text/comparing_defs.tex
--- a/text/comparing_defs.tex	Fri Oct 16 23:28:51 2009 +0000
+++ b/text/comparing_defs.tex	Fri Oct 16 23:45:27 2009 +0000
@@ -113,6 +113,7 @@
 on $C^2$ (Figure \ref{fzo1}).
 Isotopy invariance implies that this is associative.
 We will define a ``horizontal" composition later.
+\nn{maybe no need to postpone?}
 
 \begin{figure}[t]
 \begin{equation*}
@@ -168,7 +169,15 @@
 \end{figure}
 We first collapse the red region, then remove a product morphism from the boundary,
 
-\nn{postponing horizontal composition of 2-morphisms until we make up our minds about product axioms.}
+We define horizontal composition of 2-morphisms as shown in Figure \ref{fzo5}.
+It is not hard to show that this is independent of the arbitrary (left/right) choice made in the definition, and that it is associative.
+\begin{figure}[t]
+\begin{equation*}
+\mathfig{.83}{tempkw/zo5}
+\end{equation*}
+\caption{Horizontal composition of 2-morphisms}
+\label{fzo5}
+\end{figure}
 
 \nn{need to find a list of axioms for pivotal 2-cats to check}