From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7349 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Two_questions Date: Sun, 24 Jun 2012 12:37:28 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1340582787 3426 80.91.229.3 (25 Jun 2012 00:06:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 25 Jun 2012 00:06:27 +0000 (UTC) Cc: "categories" To: =?ISO-8859-1?Q?Andr=E9=22=20?= Original-X-From: majordomo@mlist.mta.ca Mon Jun 25 02:06:22 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 1Siwou-00042c-Fn for gsmc-categories@m.gmane.org; Mon, 25 Jun 2012 02:06:20 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50917) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Siwnu-0008Jf-Nk; Sun, 24 Jun 2012 21:05:18 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Siwnw-0002Zd-Ll for categories-list@mlist.mta.ca; Sun, 24 Jun 2012 21:05:20 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7349 Archived-At: Salut, Andr=E9, I'm ashamed how long it took me to come to this realization, but you were absolutely correct in your surmise that, when one lets ... > ... E' be the set obtained from E by > adding copy p' of p. There are two embeddings u,u':E-->E', > the first u is the inclusion of E in E', and the second u' is defined = > by putting u'(p)=3Dp' and u'(x)=3Dx for x different than p. =2E.. the resulting u' is the same as the result of conjugating all the v= alues of u by the transposition t that exchanges p with p'. Thus, the ... > ... pair of homomorphisms h,h':E!-->E'! the equaliser of which > is the stabiliser S(p) of p in E!. =2E.. that arises is exactly the same as the pair Sammy's argument = would adduce, and the only respect in which ... > This last argument seems to differ from the argument you have presented= =2E is that for Sammy it was enough to observe that h and h' differ SOMEWHERE= = when E is more than just {p}, while what you observe is rather more, name= ly, = that h and h' actually differ EVERYWHERE other than on S(p), i.e., that t= he = ONLY place where h and h' do NOT differ is S(p) :-) . > Am I making an error? Only in thinking that seeming difference makes any real difference :-) . I hope this clarifies matters, and I think it's worth showing categories@= mta. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]