
diff -r c9f41c18a96f -r 9dfb5db2acd7 text/ncat.tex
--- a/text/ncat.tex	Tue Sep 21 14:44:17 2010 -0700
+++ b/text/ncat.tex	Tue Sep 21 17:28:14 2010 -0700
@@ -45,7 +45,7 @@
 By ``a $k$-ball" we mean any $k$-manifold which is homeomorphic to the 
 standard $k$-ball.
 We {\it do not} assume that it is equipped with a 
-preferred homeomorphism to the standard $k$-ball, and the same applies to ``a $k$-sphere" below.
+preferred homeomorphism to the standard $k$-ball, and the same applies to ``a $k$-sphere" below. \nn{List the axiom numbers here, mentioning alternate versions, and also the same in the module section.}
 
 Given a homeomorphism $f:X\to Y$ between $k$-balls (not necessarily fixed on 
 the boundary), we want a corresponding
@@ -465,7 +465,7 @@
 same (traditional) $i$-morphism as the corresponding codimension $i$ cell $c$.
 
 
-\addtocounter{axiom}{-1}
+%\addtocounter{axiom}{-1}
 \begin{axiom}[Product (identity) morphisms]
 For each pinched product $\pi:E\to X$, with $X$ a $k$-ball and $E$ a $k{+}m$-ball ($m\ge 1$),
 there is a map $\pi^*:\cC(X)\to \cC(E)$.
@@ -592,7 +592,7 @@
 
 The revised axiom is
 
-\addtocounter{axiom}{-1}
+%\addtocounter{axiom}{-1}
 \begin{axiom}[\textup{\textbf{[plain  version]}} Extended isotopy invariance in dimension $n$.]
 \label{axiom:extended-isotopies}
 Let $X$ be an $n$-ball and $f: X\to X$ be a homeomorphism which restricts
@@ -610,7 +610,7 @@
 $C_*(\Homeo_\bd(X))$ denote the singular chains on this space.
 
 
-\addtocounter{axiom}{-1}
+%\addtocounter{axiom}{-1}
 \begin{axiom}[\textup{\textbf{[$A_\infty$ version]}} Families of homeomorphisms act in dimension $n$.]
 For each $n$-ball $X$ and each $c\in \cl{\cC}(\bd X)$ we have a map of chain complexes
 \[
@@ -1434,7 +1434,7 @@
 
 For $A_\infty$ modules we require
 
-\addtocounter{module-axiom}{-1}
+%\addtocounter{module-axiom}{-1}
 \begin{module-axiom}[\textup{\textbf{[$A_\infty$ version]}} Families of homeomorphisms act]
 For each marked $n$-ball $M$ and each $c\in \cM(\bd M)$ we have a map of chain complexes
 \[




