--- 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