--- a/text/appendixes/comparing_defs.tex	Wed Jun 01 15:04:31 2011 -0600
+++ b/text/appendixes/comparing_defs.tex	Wed Jun 01 15:17:39 2011 -0600
@@ -70,6 +70,10 @@
 the nontrivial spin homeomorphism from $B^1$ to itself which covers the identity
 gives an order 2 automorphism of $c(\cX)^1$.
 There is a similar involution on the objects $c(\cX)^0$.
+In the case where there is only one object and we are enriching over complex vector spaces, this
+is just a super algebra.
+The even elements are the $+1$ eigenspace of the involution on $c(\cX)^1$, 
+and the odd elements are the $-1$ eigenspace of the involution.
 
 For 1-categories based on $\text{Pin}_-$ balls,
 we have an order 4 antiautomorphism of $c(\cX)^1$.