From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/344 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Morphisms of diagrams Date: Tue, 18 Mar 1997 11:24:17 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016905 25297 80.91.229.2 (29 Apr 2009 14:55:05 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:05 +0000 (UTC) To: categories Original-X-From: cat-dist Tue Mar 18 11:25:03 1997 Original-Received: by mailserv.mta.ca; id AA23665; Tue, 18 Mar 1997 11:24:20 -0400 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:344 Archived-At: Date: Tue, 18 Mar 1997 10:20:19 -0500 From: Charles Wells Let C be a category and I and I' graphs (or categories if you prefer). Define a morphism of diagrams psi:(delta:I-->C)-->(delta':I'-->C) to be a graph morphism (or functor if you prefer) psi:I-->I' together with a natural transformation alpha:delta' o psi-->delta. This definition turns Lim into a contravariant functor from the category of diagrams to C (when C is complete, anyway). I believe this construction has been familiar since the early days of category theory, but I don't know a reference and would be glad to learn of any. By the way, Barr in SLN 236 (page 52) defines an entirely different notion of morphism of diagrams which Tholen and Tozzi develop extensively in "Completions of Categories and Initial Completions", Cahiers 1989, pages 127-156. This makes Lim a covariant functor. Charles Wells, 105 South Cedar Street, Oberlin, Ohio 44074, USA. (I am on sabbatical until 20 August 1997 and cannot easily be reached at Case Western Reserve University.) EMAIL: cfw2@po.cwru.edu. HOME PHONE: 216 774 1926. FAX: Same as home phone. HOME PAGE: URL http://www.cwru.edu/CWRU/Dept/Artsci/math/wells/home.html "Some have said that I can't sing. But no one will say that I _didn't_ sing." --Florence Foster Jenkins