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From: Paul B Levy
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Subject: Re: dagger vs involutive
Date: Wed, 7 Mar 2007 15:13:58 +0000 (GMT)
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Oh dear, I think I might have recently increased the set of synonyms.
A couple of years ago, in conversation with Weng Kin Ho, I suggested the
following terminology.
Involutive category:
a category C, with a functor c : C^op --> C and an isomorphism alpha : c^2
--> id_C
Strictly involutive category:
a category C with a functor c : C^op --> C such that c^2 = id_C
Locally involutive category:
a category C with an identity-on-objects functor c : C^op --> C such that
c^2 = id_C.
Weng Kin used this terminology in his PhD thesis (pp 17-18)
http://www.cs.bham.ac.uk/~wkh/papers/thesis.pdf
I wasn't aware of the other terminologies.
Paul