
diff -r 6868130229bf -r 9e695fc9b13c text/ncat.tex
--- a/text/ncat.tex	Sat Jun 25 06:52:04 2011 -0700
+++ b/text/ncat.tex	Sat Jun 25 18:14:37 2011 -0700
@@ -941,7 +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}
+Note that if we think of an ordinary 1-category as an $A_\infty$ 1-category where $k$-morphisms are identities for $k>1$,
+then Axiom \ref{axiom:families} implies Axiom \ref{axiom:extended-isotopies}.
 
 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} 




