--- a/text/ncat.tex	Thu Sep 23 10:03:26 2010 -0700
+++ b/text/ncat.tex	Thu Sep 23 12:34:16 2010 -0700
@@ -1845,7 +1845,7 @@
 	\draw[line width=1pt, green!50!brown, ->] (M\n.\qm+135) to[out=\qm+135,in=\qm+90] (\qm+5:1.3);
 }
 \end{tikzpicture}
-\caption{Cone on a marked circle}
+\caption{Cone on a marked circle, the prototypical 1-marked ball}
 \label{feb21d}
 \end{figure}
 
@@ -2237,9 +2237,11 @@
 
 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}
+%\nn{still to do: associativity}
 
 \medskip