--- a/blob to-do	Sat Jun 25 06:44:35 2011 -0700
+++ b/blob to-do	Sat Jun 25 06:52:04 2011 -0700
@@ -1,6 +1,8 @@
 
 ====== big ======
 
+* need to fix fam-o-homeo argument per discussion with Rob
+
 * need to change module axioms to follow changes in n-cat axioms; search for and destroy all the "Homeo_\bd"'s, add a v-cone axiom
 
 * probably should go through and refer to new splitting axiom when we need to choose refinements etc.

--- a/text/ncat.tex	Sat Jun 25 06:44:35 2011 -0700
+++ b/text/ncat.tex	Sat Jun 25 06:52:04 2011 -0700
@@ -932,6 +932,7 @@
 And indeed, this is true for our main example of an $A_\infty$ $n$-category based on the blob construction.
 Stating this sort of compatibility for general $\cS$ and $\cJ$ requires further assumptions, 
 such as the forgetful functor from $\cS$ to sets having a left adjoint, and $\cS$ having an internal Hom.
+
 An alternative (due to Peter Teichner) is to say that Axiom \ref{axiom:families} 
 supersedes the $k=n$ case of Axiom \ref{axiom:morphisms}; in dimension $n$ we just have a
 functor $\bbc \to \cS$ of $A_\infty$ 1-categories.
@@ -940,6 +941,8 @@
 to refrain from settling on a preferred version of the axiom until
 we have a greater variety of examples to guide the choice.
 
+\nn{say something about isotopy invariance being a special case}
+
 Another variant of the above axiom would be to drop the ``up to homotopy" and require a strictly associative action. 
 In fact, the alternative construction of the blob complex described in \S \ref{ss:alt-def} 
 gives $n$-categories as in Example \ref{ex:blob-complexes-of-balls} which satisfy this stronger axiom;