From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3629 Path: news.gmane.org!not-for-mail From: "Jamie Vicary" Newsgroups: gmane.science.mathematics.categories Subject: Equalisers and coequalisers in categories with a \dag-involution Date: Wed, 14 Feb 2007 22:13:59 +0000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019420 9538 80.91.229.2 (29 Apr 2009 15:37:00 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:00 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Feb 14 20:23:49 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 14 Feb 2007 20:23:49 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HHUFL-0001TC-40 for categories-list@mta.ca; Wed, 14 Feb 2007 20:13:11 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 22 Original-Lines: 23 Xref: news.gmane.org gmane.science.mathematics.categories:3629 Archived-At: Dear all, Consider the following straightforward coequaliser (e,E) formed by f,g:A-->B and e:B-->E, with e.f=e.g. I am working in a category with biproducts, and with a contravariant involutive endofunctor (--)^\dag on the category which is compatible with the biproducts; i.e. (projection)^\dag = injection for all projections and injections making up a part of a biproduct. In such a category, it is natural to consider the coequaliser object E to be the subspace of B on which the morphisms f and g agree. It is therefore natural to require e.(e^\dag) = id_E; this sort of condition is similar to the sorts of conditions that form part of the definition of the biproduct. I'm asking whether there exists a natural framework generalising the theory of biproducts, which is analagous to the way that (co)limits generalise (co)products, within which I can safely assume that e.(e^\dag) = id_E. Biproducts seem quite different from products and coproducts, though, so I don't know how it would work. Jamie Vicary.