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/ ]