From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7341 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Two questions Date: Thu, 21 Jun 2012 09:34:13 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; format=flowed; charset=US-ASCII X-Trace: dough.gmane.org 1340297550 32654 80.91.229.3 (21 Jun 2012 16:52:30 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 21 Jun 2012 16:52:30 +0000 (UTC) Cc: Bob Raphael To: Categories list Original-X-From: majordomo@mlist.mta.ca Thu Jun 21 18:52:29 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 1ShkcM-0002lR-HE for gsmc-categories@m.gmane.org; Thu, 21 Jun 2012 18:52:26 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51590) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1ShkbY-0005UJ-0s; Thu, 21 Jun 2012 13:51:36 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ShkbY-000143-KJ for categories-list@mlist.mta.ca; Thu, 21 Jun 2012 13:51:36 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7341 Archived-At: Googling around, I have come on several claims that there are no non-trivial injectives in the category of groups (e.g., Mac Lane in the 1950 Duality for groups paper credits Baer with an elegant proof, but gives no hint of what it might be and Baer's earlier paper on injectives doesn't mention it). I have not come on any proof of this, however. Somewhere I have seen a proof that all monics in the category of groups are regular. I think it was in a paper by Eilenberg and ??? and it needed a special argument if there were elements of order 2. Can someone help me find this? Michael -- The United States has the best congress money can buy. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]