--- a/text/ncat.tex	Thu Sep 23 13:08:25 2010 -0700
+++ b/text/ncat.tex	Thu Sep 23 18:10:35 2010 -0700
@@ -2079,7 +2079,7 @@
 Let $D' = B\cap C$.
 It is not hard too show that the above two maps are mutually inverse.
 
-\begin{lem}
+\begin{lem} \label{equator-lemma}
 Any two choices of $E$ and $E'$ are related by a series of modifications as above.
 \end{lem}
 
@@ -2237,15 +2237,4 @@
 
 To define (binary) composition of $n{+}1$-morphisms, choose the obvious common equator
 then compose the module maps.
-Associativity of this composition rules follows from repeated application of the adjoint identity between
-the maps of Figures \ref{jun23b} and \ref{jun23c}.
-
-
-%\nn{still to do: associativity}
-
-\medskip
-
-%\nn{Stuff that remains to be done (either below or in an appendix or in a separate section or in
-%a separate paper): discuss Morita equivalence; functors}
-
-
+The proof that this composition rule is associative is similar to the proof of Lemma \ref{equator-lemma}.