...
Binary file diagrams/pdf/tempkw/zo5.pdf has changed
--- 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}