From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8148 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Is this known? Date: Tue, 3 Jun 2014 11:36:27 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1401839931 18230 80.91.229.3 (3 Jun 2014 23:58:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 3 Jun 2014 23:58:51 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Wed Jun 04 01:58:46 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1WrybM-0003vx-4r for gsmc-categories@m.gmane.org; Wed, 04 Jun 2014 01:58:44 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:34129) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1WryaT-0006p4-Qs; Tue, 03 Jun 2014 20:57:49 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1WryaT-0000IC-GP for categories-list@mlist.mta.ca; Tue, 03 Jun 2014 20:57:49 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8148 Archived-At: In the course of certain studies on commutative rings, we needed the following result (to be sure, for ideals, not congruences): Let \Csc be a regular category and $f:A\to B$ an epimorphism in \Csc. Suppose $E_1$ and $E_2$ are congruences on $B$ with $D_1$ and $D_2$ their inverse images under $f\x f$. If the induced $A/D_1\to B/E_1$ is an isomorphism and $D_1\inc D_2$, then $E_1\inc E_2$ Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]