From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7350 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 21:34:20 -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 1340631041 6124 80.91.229.3 (25 Jun 2012 13:30:41 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 25 Jun 2012 13:30:41 +0000 (UTC) Cc: "categories" To: =?ISO-8859-1?Q?=22Joyal=20Andr=E9=22=20?= Original-X-From: majordomo@mlist.mta.ca Mon Jun 25 15:30:36 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 1Sj9ND-0008Ir-Pm for gsmc-categories@m.gmane.org; Mon, 25 Jun 2012 15:30:35 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:51033) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1Sj9MJ-0004TU-B3; Mon, 25 Jun 2012 10:29:39 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Sj9MJ-0005qo-DL for categories-list@mlist.mta.ca; Mon, 25 Jun 2012 10:29:39 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7350 Archived-At: Correction/clarification to previous note: in what follows, the sloppy ph= rase > ... the resulting u' is the same as the result of conjugating all the v= alues of u by the transposition ... should be replaced by the more accurate expanded version > ... the h' (as below) resulting from u' is the same as what Sammy gets = by conjugating all the values of the h that arises from u by the transpositi= on =2E.. = Sorry for the sloppy writing. = Cheers, -- Fred ------ Original Message ------ Received: Sun, 24 Jun 2012 08:09:45 PM EDT From: "Fred E.J. Linton" To: Andr=E9" Cc: "categories" Subject: categories: Re: Two_questions > 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. > = > ... the resulting u' is the same as the result of conjugating all the values > 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!. > = > ... 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 present= ed. > = > is that for Sammy it was enough to observe that h and h' differ SOMEWHE= RE = > when E is more than just {p}, while what you observe is rather more, na= mely, > that h and h' actually differ EVERYWHERE other than on S(p), i.e., that= the > 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 :-) = =2E > = > Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]