--- a/preamble.tex Wed Sep 15 13:30:15 2010 -0500
+++ b/preamble.tex Wed Sep 15 13:33:14 2010 -0500
@@ -62,8 +62,8 @@
\newtheorem*{defn*}{Definition} % unnumbered definition
\newtheorem{question}{Question}
\newtheorem{property}{Property}
-\newtheorem{axiom}{Axiom}
-\newtheorem{module-axiom}{Module Axiom}
+\newtheorem{axiom}{Axiom}[section]
+\newtheorem{module-axiom}{Module Axiom}[section]
\newenvironment{rem}{\noindent\textsl{Remark.}}{} % perhaps looks better than rem above?
\newtheorem{rem*}[prop]{Remark}
\newtheorem{remark}[prop]{Remark}
--- a/text/ncat.tex Wed Sep 15 13:30:15 2010 -0500
+++ b/text/ncat.tex Wed Sep 15 13:33:14 2010 -0500
@@ -1093,8 +1093,7 @@
\end{itemize}
In other words, we have a zig-zag of equivalences starting at $a$ and ending at $\hat{a}$.
The idea of the proof is to produce a similar zig-zag where everything antirefines to the same
-disjoint union of balls, and then invoke the associativity axiom \ref{nca-assoc}.
-\nn{hmmm... it would be nicer if this were ``7.xx" instead of ``4"}
+disjoint union of balls, and then invoke Axiom \ref{nca-assoc} which ensures associativity.
Let $z$ be a decomposition of $W$ which is in general position with respect to all of the
$x_i$'s and $v_i$'s.