From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5332 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Simple Situation Date: Mon, 7 Dec 2009 15:37:33 +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: ger.gmane.org 1260237031 16868 80.91.229.12 (8 Dec 2009 01:50:31 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Tue, 8 Dec 2009 01:50:31 +0000 (UTC) To: "Ellis D. Cooper" , categories@mta.ca Original-X-From: categories@mta.ca Tue Dec 08 02:50:23 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1NHpDX-0001co-KC for gsmc-categories@m.gmane.org; Tue, 08 Dec 2009 02:50:19 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NHog6-0001yX-EE for categories-list@mta.ca; Mon, 07 Dec 2009 21:15:46 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5332 Archived-At: If I've understood it right, this is exactly the concept of a "multi-terminal object" (that is, a multi-limit for the empty diagram). The name is due to me (in a paper called "A syntactic approach to Diers's localizable categories" in SLNM 753 (1979)), but the concept is due to Yves Diers: see his "Familles universelles de morphismes", Ann. Soc. Sci. Bruxelles 93 (1979). Peter Johnstone On Fri, 4 Dec 2009, Ellis D. Cooper wrote: > Dear categorists, > > Let C be a category with a distinguished sub-category E and a > distinguished family S of morphisms > such that for every object x of C there is a unique morphism f_x: x > ---> e_x with e_x an object of E > so that the following conditions are satisfied: (1) if x is in E then > f_x = 1_x (the identity morphism > of x), (2) if s: x ---> y is in S then e_y = e_x and f_x = f_y s. > > Hasn't this simple situation been named and incorporated in some > publication on category > theory? A reference would be most appreciated. > > Ellis D. Cooper > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]