From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6368 Path: news.gmane.org!not-for-mail From: "Fred E.J. Linton" Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminological question, and more Date: Fri, 05 Nov 2010 19:12:09 -0400 Message-ID: Reply-To: "Fred E.J. Linton" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1289048358 11411 80.91.229.12 (6 Nov 2010 12:59:18 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 6 Nov 2010 12:59:18 +0000 (UTC) To: "categories" Original-X-From: majordomo@mlist.mta.ca Sat Nov 06 13:59:13 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PEiMT-0000H1-EX for gsmc-categories@m.gmane.org; Sat, 06 Nov 2010 13:59:13 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:40322) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PEiLz-0006EY-KK; Sat, 06 Nov 2010 09:58:43 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PEiLw-0007iK-UT for categories-list@mlist.mta.ca; Sat, 06 Nov 2010 09:58:41 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6368 Archived-At: Thanks to all who've responded. > I've been asked for "... the name given in an arbitrary category > to an object A for which every mono B----->A is an isomorphism." Peter Johnstone has suggested that such an object (whose poset of subobjects reduces to just the object itself) is simply "minimal". And I'm embarrassed at having lost so much of my former grasp of Galois theory: > ... whether "the inclusion Q >-------> R of > the ring of rational numbers into that of real ones is a bimorphism, in= the > category Rng of rings with units and units preserving ring homomorphism= s." > > Reflexively I think: monic, yes; epic, no, as permuting any two indepen= dent > transcendentals should extend to a non-identity automorphism of R over = Q. No! There is no "non-identity automorphism of R over Q." Fortunately, as Mike Barr and George Janelidze have pointed out, each permutation of a= = transcendence basis of R over Q extends to an injection, over Q, of R = into its algebraic closure C, which is good enough. Cheers, and thanks again, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]