From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9508 Path: news.gmane.org!.POSTED!not-for-mail From: David Yetter Newsgroups: gmane.science.mathematics.categories Subject: Products of epimorphisms Date: Fri, 19 Jan 2018 19:20:04 +0000 Message-ID: Reply-To: David Yetter NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: blaine.gmane.org 1516408320 21107 195.159.176.226 (20 Jan 2018 00:32:00 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 20 Jan 2018 00:32:00 +0000 (UTC) To: "categories@mta.ca" Original-X-From: majordomo@mlist.mta.ca Sat Jan 20 01:31:56 2018 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1ech4O-0004Ku-Ub for gsmc-categories@m.gmane.org; Sat, 20 Jan 2018 01:31:41 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:59858) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ech7E-0006Y9-NZ; Fri, 19 Jan 2018 20:34:36 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ech5y-0001iZ-6f for categories-list@mlist.mta.ca; Fri, 19 Jan 2018 20:33:18 -0400 Thread-Topic: Products of epimorphisms Thread-Index: AQHTkVlJfp+BjuxAsk6SI9O0MsXGgg== Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9508 Archived-At: Dear fellow category theorists, I'm interested in finding out at what level of generality a result that pla= inly holds in Sets (and Sets^op) is true: Given two epimorphisms f:A-->>B and g:C-->D, the square formed by f x 1_C, = 1_A x g, f x 1_D and=20 1_B x D is a pushout. I'd like it to be true (at least) in toposes and I think I have an element-= wise proof (but don't remember the details of the semantics given by, for i= nstance, Osius, well enough to be sure I've really proven the result in all= toposes -- it's been years since I thought seriously about that sort of th= ing). And, is there anywhere in the literature that this occurs? It feels like t= he sort of thing that would have been known long ago. Best Thoughts, David Yetter Professor of Mathematics Kansas State University [For admin and other information see: http://www.mta.ca/~cat-dist/ ]