Re: Quantum computation and categories

[John Baez <john.c.baez@gmail.com>]

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


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