# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1310330599 21600
# Node ID cbfbcf204016af2502238d0c2c5a495d66a31828
# Parent  7dc75375d376b8e334550cf37c6f7b729581a447
no splittability requirement for k=n

diff -r 7dc75375d376 -r cbfbcf204016 blob to-do
--- 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
diff -r 7dc75375d376 -r cbfbcf204016 text/ncat.tex
--- 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.