From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/970 Path: news.gmane.org!not-for-mail From: "Dr. P.T. Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Inferring colimits Date: Wed, 16 Dec 1998 10:55:59 +0000 (GMT) Message-ID: References: <9812152331.AA08574@decserv2> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017399 28619 80.91.229.2 (29 Apr 2009 15:03:19 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:03:19 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Wed Dec 16 11:41:10 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id IAA32019 for categories-list; Wed, 16 Dec 1998 08:57:28 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f In-Reply-To: <9812152331.AA08574@decserv2> from "David B. Benson" at Dec 15, 98 03:31:54 pm X-Mailer: ELM [version 2.4 PL25] Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:970 Archived-At: > Now for the question. Has there been any systematic study of what > I have just defined as repletions? If not, are there in any case some papers > I should consider? I think the question as posed by David (relative to a particular category, in which some but not all diagrams of a particular shape may have colimits) is a very hard one. A lot is known about inferring the existence of particular types of colimits, in arbitrary categories, from the existence of other types: see the paper by Albert and Kelly "The closure of a class of colimits" in JPAA 51 (1988), and subsequent references of which Max will no doubt remind us. But when you work in a particular category, there are so many ways of "mutilating" the category by omitting particular objects which are required as the vertices of colimit cones, that I suspect there is almost nothing you can say in general. Incidentally, a similar comment applies to David's paper "Multilinearity of sketches" in TAC 3 (1997): I tried to make this point in my review (MR 98j:18006). Peter Johnstone