Toby wrote: John Baez wrote in part:
A dagger-category is a category C with a functor F: C -> C^{op} which is the identity on objects and has F^2 = 1.
Category theorists will note that the above definition is "evil", in the technical sense of that term....
By default, there is a non-evil way to say it:
Given a category C, a _non-evil dagger-category structure_ on C consists of a dagger-category C' and an equivalence F: C -> C' of categories.
Yes, you can do that. But Jacob Lurie has argued (in email to me) that the resulting notion is problematic. So, he took a different tack in his work on the cobordism hypothesis. I'd need to review that email to say more... Best, jb [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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John Baez