From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6066 Path: news.gmane.org!not-for-mail From: John Kennison Newsgroups: gmane.science.mathematics.categories Subject: RE: Question on choosing subobjects consistently Date: Sat, 28 Aug 2010 06:10:39 -0400 Message-ID: References: Reply-To: John Kennison NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1283001318 32511 80.91.229.12 (28 Aug 2010 13:15:18 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 28 Aug 2010 13:15:18 +0000 (UTC) To: Michael Barr , Categories list Original-X-From: majordomo@mlist.mta.ca Sat Aug 28 15:15:16 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 1OpLFc-0005Yc-67 for gsmc-categories@m.gmane.org; Sat, 28 Aug 2010 15:15:16 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50643) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OpLCR-00028t-2E; Sat, 28 Aug 2010 10:11:59 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OpLCN-0007HK-Mb for categories-list@mlist.mta.ca; Sat, 28 Aug 2010 10:11:55 -0300 Thread-Topic: categories: Question on choosing subobjects consistently In-Reply-To: Accept-Language: en-US Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6066 Archived-At: When Grothendieck says to "choose sub objects" what does he mean since a su= bobjrcts is an equivalence class of monos? If he means to choose monos into= each object such that each subobject is represented by a unique chosen mon= o and a composition of two chosen monos is again a chosen mono, then this i= s false as there are counter examples. There can be thre objects A B C such= that there are two nonequivalent monos from B to C and a mono from A to B = such that when you compse the mono from A to B with the monos from B to C y= ou get equivalent monos tom A to C representing the same sub object of C. ________________________________________ From: Michael Barr [barr@math.mcgill.ca] Sent: Thursday, August 26, 2010 6:09 PM To: Categories list Subject: categories: Question on choosing subobjects consistently 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/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]