--- a/text/ncat.tex	Tue Jul 05 13:28:02 2011 -0600
+++ b/text/ncat.tex	Sun Jul 10 14:43:19 2011 -0600
@@ -781,7 +781,7 @@
 
 \begin{axiom}[Splittings]
 \label{axiom:vcones}
-Let $c\in \cC_k(X)$ and
+Let $c\in \cC_k(X)$, with $0\le k < n$, and
 let $P$ be a finite poset of splittings of $c$.
 Then we can embed $\vcone(P)$ into the splittings of $c$, with $P$ corresponding to the base of $\vcone(P)$.
 Furthermore, if $q$ is any decomposition of $X$, then we can take the vertex of $\vcone(P)$ to be $q$ up to a small perturbation.