
diff -r 52309e058a95 -r 2252c53bd449 text/ncat.tex
--- a/text/ncat.tex	Sat May 29 23:13:03 2010 -0700
+++ b/text/ncat.tex	Sat May 29 23:13:20 2010 -0700
@@ -86,6 +86,7 @@
 Morphisms are modeled on balls, so their boundaries are modeled on spheres:
 
 \begin{axiom}[Boundaries (spheres)]
+\label{axiom:spheres}
 For each $0 \le k \le n-1$, we have a functor $\cC_k$ from 
 the category of $k$-spheres and 
 homeomorphisms to the category of sets and bijections.
@@ -735,7 +736,7 @@
 (actions of homeomorphisms);
 define $k$-cat $\cC(\cdot\times W)$}
 
-Recall that Axiom \ref{} for an $n$-category provided functors $\cC$ from $k$-spheres to sets for $0 \leq k < n$. We claim now that these functors automatically agree with the colimits we have associated to spheres in this section. \todo{} \todo{In fact, we probably should do this for balls as well!} For the remainder of this section we will write $\underrightarrow{\cC}(W)$ for the colimit associated to an arbitary manifold $W$, to distinguish it, in the case that $W$ is a ball or a sphere, from $\cC(W)$, which is part of the definition of the $n$-category. After the next three lemmas, there will be no further need for this notational distinction.
+Recall that Axiom \ref{axiom:spheres} for an $n$-category provided functors $\cC$ from $k$-spheres to sets for $0 \leq k < n$. We claim now that these functors automatically agree with the colimits we have associated to spheres in this section. \todo{} \todo{In fact, we probably should do this for balls as well!} For the remainder of this section we will write $\underrightarrow{\cC}(W)$ for the colimit associated to an arbitary manifold $W$, to distinguish it, in the case that $W$ is a ball or a sphere, from $\cC(W)$, which is part of the definition of the $n$-category. After the next three lemmas, there will be no further need for this notational distinction.
 
 \begin{lem}
 For a $k$-ball or $k$-sphere $W$, with $0\leq k < n$, $$\underrightarrow{\cC}(W) = \cC(W).$$




