--- a/text/appendixes/comparing_defs.tex	Wed Mar 23 15:33:48 2011 -0700
+++ b/text/appendixes/comparing_defs.tex	Wed Mar 23 15:52:36 2011 -0700
@@ -48,12 +48,12 @@
 The base case is for oriented manifolds, where we obtain no extra algebraic data.
 
 For 1-categories based on unoriented manifolds, 
-there is a map $*:c(\cX)^1\to c(\cX)^1$
+there is a map $\dagger:c(\cX)^1\to c(\cX)^1$
 coming from $\cX$ applied to an orientation-reversing homeomorphism (unique up to isotopy) 
 from $B^1$ to itself.
 Topological properties of this homeomorphism imply that 
-$a^{**} = a$ (* is order 2), * reverses domain and range, and $(ab)^* = b^*a^*$
-(* is an anti-automorphism).
+$a^{\dagger\dagger} = a$ ($\dagger$ is order 2), $\dagger$ reverses domain and range, and $(ab)^\dagger = b^\dagger a^\dagger$
+($\dagger$ is an anti-automorphism).
 
 For 1-categories based on Spin manifolds,
 the the nontrivial spin homeomorphism from $B^1$ to itself which covers the identity

--- a/text/ncat.tex	Wed Mar 23 15:33:48 2011 -0700
+++ b/text/ncat.tex	Wed Mar 23 15:52:36 2011 -0700
@@ -37,7 +37,7 @@
 
 Strictly speaking, before we can state the axioms for $k$-morphisms we need all the axioms 
 for $k{-}1$-morphisms.
-So readers who prefer things to be presented in a strictly logical order should read this subsection $n$ times, first imagining that $k=0$, then that $k=1$, and so on until they reach $k=n$.
+Readers who prefer things to be presented in a strictly logical order should read this subsection $n+1$ times, first setting $k=0$, then $k=1$, and so on until they reach $k=n$.
 
 \medskip
 
@@ -831,6 +831,9 @@
 we identify $W$ and $W'$ if $\bd W = \bd W'$ and there is a homeomorphism
 $W \to W'$ which restricts to the identity on the boundary.
 \end{example}
+\begin{remark}
+Working with the smooth bordism category would require careful attention to either collars, corners or halos.
+\end{remark}
 
 %\nn{the next example might be an unnecessary distraction.  consider deleting it.}