# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1300234964 25200
# Node ID e27bc92e5d9ba5374497b246f7369cf618760f0b
# Parent  3d751b59a7d8aa40383ca07c9f5c56a02835de87
explain why we dont require gluing to be surjective

diff -r 3d751b59a7d8 -r e27bc92e5d9b text/ncat.tex
--- a/text/ncat.tex	Tue Mar 15 17:11:47 2011 -0700
+++ b/text/ncat.tex	Tue Mar 15 17:22:44 2011 -0700
@@ -205,6 +205,12 @@
 The lemma follows from Definition \ref{def:colim-fields} and Lemma \ref{lem:colim-injective}.
 %\nn{we might want a more official looking proof...}
 
+We do not insist on surjectivity of the gluing map, since this is not satisfied by all of the examples
+we are trying to axiomatize.
+If our $k$-morphisms $\cC(X)$ are labeled cell complexes embedded in $X$, then a $k$-morphism is
+in the image of the gluing map precisely which the cell complex is in general position
+with respect to $E$.
+
 If $S$ is a 0-sphere (the case $k=1$ above), then $S$ can be identified with the {\it disjoint} union
 of two 0-balls $B_1$ and $B_2$ and the colimit construction $\cl{\cC}(S)$ can be identified
 with the (ordinary, not fibered) product $\cC(B_1) \times \cC(B_2)$.