From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7344 Path: news.gmane.org!not-for-mail From: Peter LeFanu Lumsdaine Newsgroups: gmane.science.mathematics.categories Subject: Re: Two questions Date: Thu, 21 Jun 2012 21:25:12 -0300 Message-ID: References: Reply-To: Peter LeFanu Lumsdaine NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1340360091 15839 80.91.229.3 (22 Jun 2012 10:14:51 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 22 Jun 2012 10:14:51 +0000 (UTC) Cc: Andrej Bauer To: Categories list Original-X-From: majordomo@mlist.mta.ca Fri Jun 22 12:14:51 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.80]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Si0t8-0001TB-Aq for gsmc-categories@m.gmane.org; Fri, 22 Jun 2012 12:14:50 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50208) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Si0sb-0007XG-9u; Fri, 22 Jun 2012 07:14:17 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Si0sa-0004Yl-Ps for categories-list@mlist.mta.ca; Fri, 22 Jun 2012 07:14:16 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7344 Archived-At: On Thu, Jun 21, 2012 at 2:54 PM, Michael Shulman wrote: > On Thu, Jun 21, 2012 at 6:34 AM, Michael Barr wrote= : >> Somewhere I have seen a proof that all monics in the category of groups >> are regular. =C2=A0I think it was in a paper by Eilenberg and ??? and it= needed >> a special argument if there were elements of order 2. =C2=A0Can someone = help me >> find this? > > I don't know the original reference, but this is exercise 7H in The > Joy of Cats, which contains a substantial hint for a proof (not > involving a special case for order-2 elements, so maybe it is a > different proof). There was some discussion of this a couple of years ago on Andrej Bauer=E2=80=99s blog and mathoverflow: http://math.andrej.com/2010/11/10/subgroups-are-equalizers-constructively/ http://mathoverflow.net/questions/41208/are-all-group-monomorphisms-regular= -constructively/ (the chronology/causality between the two is a little non-obvious: the MO question predates the blog post, but the eventual solution at MO follows it) The discussion there is on proving this constructively, but as often, the first step is looking at the classical proof with a magnifying glass. =E2=80=93p. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]