--- a/text/comparing_defs.tex	Fri Oct 16 23:45:27 2009 +0000
+++ b/text/comparing_defs.tex	Sun Oct 18 23:54:43 2009 +0000
@@ -97,6 +97,8 @@
 Each approach has advantages and disadvantages.
 For better or worse, we choose bigons here.}
 
+\nn{maybe we should do both rectangles and bigons?}
+
 Define the $k$-morphisms $C^k$ of $C$ to be $\cC(B^k)_E$, where $B^k$ denotes the standard
 $k$-ball, which we also think of as the standard bihedron.
 Since we are thinking of $B^k$ as a bihedron, we have a standard decomposition of the $\bd B^k$

--- 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.