# HG changeset patch
# User Kevin Walker <kevin@canyon23.net>
# Date 1306963059 21600
# Node ID 966a571daa10f6bf289453606ccd7bace11b99ce
# Parent  c5a33223af00fa08519ff6fa4e126f6b8d7883fd
added remark on super algebra

diff -r c5a33223af00 -r 966a571daa10 blob to-do
--- a/blob to-do	Wed Jun 01 15:04:31 2011 -0600
+++ b/blob to-do	Wed Jun 01 15:17:39 2011 -0600
@@ -14,11 +14,6 @@
 
 * ** new material in colimit section needs a proof-read
 
-* In the appendix on n=1, explain more about orientations. Also say
-what happens on objects for spin manifolds: the unique point has an
-automorphism, which translates into a involution on objects. Mention
-super-stuff. [partly done]
-
 
 * should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable
 
diff -r c5a33223af00 -r 966a571daa10 blob_changes_v3
--- a/blob_changes_v3	Wed Jun 01 15:04:31 2011 -0600
+++ b/blob_changes_v3	Wed Jun 01 15:17:39 2011 -0600
@@ -24,6 +24,7 @@
 - reduced intermingling for the various n-cat definitions (plain, enriched, A-infinity)
 - strengthened n-cat isotopy invariance axiom to allow for homeomorphisms which act trivially elements on the restriction of an n-morphism to the boundary of the ball
 - more details on axioms for enriched n-cats
+- added details to the construction of traditional 1-categories from disklike 1-categories (Appendix C.1)
 - 
 
 
diff -r c5a33223af00 -r 966a571daa10 text/appendixes/comparing_defs.tex
--- 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 $c(\cX)^1$.