From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3670 Path: news.gmane.org!not-for-mail From: Paul B Levy Newsgroups: gmane.science.mathematics.categories Subject: Re: dagger vs involutive Date: Wed, 7 Mar 2007 15:13:58 +0000 (GMT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019446 9714 80.91.229.2 (29 Apr 2009 15:37:26 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:26 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 7 19:29:32 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 07 Mar 2007 19:29:32 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HP5YR-0002zt-Rw for categories-list@mta.ca; Wed, 07 Mar 2007 19:28:20 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 24 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:3670 Archived-At: 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