From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2987 Path: news.gmane.org!not-for-mail From: Andree Ehresmann Newsgroups: gmane.science.mathematics.categories Subject: Partial answer to Jean Benabou Date: Wed, 11 Jan 2006 19:00:53 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: ger.gmane.org 1241019025 6771 80.91.229.2 (29 Apr 2009 15:30:25 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:25 +0000 (UTC) To: Categories Original-X-From: rrosebru@mta.ca Wed Jan 11 21:08:31 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 11 Jan 2006 21:08:31 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1EwqpI-0003Ar-TO for categories-list@mta.ca; Wed, 11 Jan 2006 21:00:28 -0400 User-Agent: Internet Messaging Program (IMP) 3.2.6 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 13 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:2987 Archived-At: In answer to the question raised by Jean: >if C is a category, what does one need to assume on a subcategory V of C to be able to construct an analogous C/V and what structure does it inherit ? Charles Ehresmann had studied the problem of the existence of a quotient = (or at least 'quasi-quotient') category of a category by a sub-category, which h= ad led to the introduction of the notion of a "proper subcategory" (generalizing distinguished sub-groups). His results, summarized in a Note (CRAS Paris= 260, 2116) are developed in the paper on non-abelian cohomology "Cohomologie a valeurs dans une categorie dominee" (Collloque Topologie Bruxelles, CBRM = 1866) . Both papers are reprinted in "Charles Ehresmann: Oeuvres completes et commentees" Part III-2 (and partially taken back in his book "Categories = et structures", Dunod 1965). With all my best wishes Andree Ehresmann.