From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6363 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminological question, and more Date: Fri, 5 Nov 2010 09:55:57 +0000 (GMT) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: dough.gmane.org 1289048121 10565 80.91.229.12 (6 Nov 2010 12:55:21 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 6 Nov 2010 12:55:21 +0000 (UTC) Cc: categories To: "Fred E.J. Linton" Original-X-From: majordomo@mlist.mta.ca Sat Nov 06 13:55:17 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 1PEiIe-0006u9-8f for gsmc-categories@m.gmane.org; Sat, 06 Nov 2010 13:55:16 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:44548) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PEiIC-0005gq-ER; Sat, 06 Nov 2010 09:54:48 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PEiIA-0007b6-G7 for categories-list@mlist.mta.ca; Sat, 06 Nov 2010 09:54:46 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6363 Archived-At: On Wed, 3 Nov 2010, Fred E.J. Linton wrote: > 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." > > I'm stumped. Any ideas? > The obvious thing is to borrow a word from ordered set theory and call it a minimal object. (All morphisms in a poset are monic.) The term "strict initial object" is well-established for an initial object 0 such that *every* morphism A --> 0 is an isomorphism. I've sometimes been tempted to use "strict object" for this property without the assumption of initiality; but the trouble is that you then have to say "costrict object" for the dual property, which doesn't seem right. Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]