From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6065 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Question on choosing subobjects consistently Date: Thu, 26 Aug 2010 18:09:20 -0400 (EDT) Message-ID: Reply-To: Michael Barr NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1282932482 11689 80.91.229.12 (27 Aug 2010 18:08:02 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 27 Aug 2010 18:08:02 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Fri Aug 27 20:08:01 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Op3LK-0006Wz-Hc for gsmc-categories@m.gmane.org; Fri, 27 Aug 2010 20:07:58 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:59851) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Op3JG-0003vf-DD; Fri, 27 Aug 2010 15:05:50 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Op3JD-0000DR-A3 for categories-list@mlist.mta.ca; Fri, 27 Aug 2010 15:05:47 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6065 Archived-At: In his Tohoku paper, Grothendieck asserted with no proof that in any category it is possible to choose subobjects for each object so that each monomorphism is isomorphic to a unique subobject of the codomain and in such a way that a subobject of a subobject of an object is also one of the chosen subobjects of the original objects. Maybe I am being dense, but I don't see how this is always possible. Does anyone on the list? I also don't see what possible value there is in making such a choice, but this doubtless was not clear in 1957. The translation (and revision) is coming along fine and I expect to release it within a month. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]