--- a/blob to-do Tue Jul 05 13:28:02 2011 -0600
+++ b/blob to-do Sun Jul 10 14:43:19 2011 -0600
@@ -1,8 +1,6 @@
====== big ======
-* reconcile splittability with A-inf/families of maps examples
-
* better discussion of systems of fields from disk-like n-cats
* need to fix fam-o-homeo argument per discussion with Rob
--- 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.