--- a/text/ncat.tex	Fri May 13 21:01:03 2011 -0700
+++ b/text/ncat.tex	Fri May 13 21:16:40 2011 -0700
@@ -1067,6 +1067,7 @@
 Inductively, we may assume that we have already defined the colimit $\cl\cC(M)$ for $k{-}1$-manifolds $M$.
 (To start the induction, we define $\cl\cC(M)$, where $M = \du_a P_a$ is a 0-manifold and each $P_a$ is
 a 0-ball, to be $\prod_a \cC(P_a)$.)
+We also assume, inductively, that we have gluing and restriction maps for colimits of $k{-}1$-manifolds.
 
 Let $\du_a X_a = M_0\to\cdots\to M_m = W$ be a ball decomposition compatible with $x$.
 Let $\bd M_i = N_i \cup Y_i \cup Y'_i$, where $Y_i$ and $Y'_i$ are glued together to produce $M_{i+1}$.
@@ -1099,8 +1100,6 @@
 If $x$ is a refinement of $y$, the map $\psi_{\cC;W}(x) \to \psi_{\cC;W}(y)$ is given by the composition maps of $\cC$.
 
 
-\nn{...}
-
 \nn{to do: define splittability and restrictions for colimits}
 
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