
diff -r 42ca1dee3441 -r 0387384c9acd text/ncat.tex
--- a/text/ncat.tex	Fri Oct 16 23:45:27 2009 +0000
+++ b/text/ncat.tex	Sun Oct 18 23:54:43 2009 +0000
@@ -242,6 +242,14 @@
 For the moment, I'll assume that all flavors of the product are at
 our disposal, and I'll plan on revising the axioms later.}
 
+\nn{current idea for fixing this: make the above axiom a ``preliminary version"
+(as we have already done with some of the other axioms), then state the official
+axiom for maps $\pi: E \to X$ which are almost fiber bundles.
+one option is to restrict E to be a (full/half/not)-pinched product (up to homeo).
+the alternative is to give some sort of local criterion for what's allowed.
+state a gluing axiom for decomps $E = E'\cup E''$ where all three are of the correct type.
+}
+
 All of the axioms listed above hold for both ordinary $n$-categories and $A_\infty$ $n$-categories.
 The last axiom (below), concerning actions of 
 homeomorphisms in the top dimension $n$, distinguishes the two cases.




