From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3498 Path: news.gmane.org!not-for-mail From: Jiri Adamek Newsgroups: gmane.science.mathematics.categories Subject: A question about extensive categories Date: Wed, 29 Nov 2006 15:58:12 +0100 (CET) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019343 9018 80.91.229.2 (29 Apr 2009 15:35:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:35:43 +0000 (UTC) To: categories net Original-X-From: rrosebru@mta.ca Wed Nov 29 15:37:29 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 29 Nov 2006 15:37:29 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GpV54-0002YR-NP for categories-list@mta.ca; Wed, 29 Nov 2006 15:26:54 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 10 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:3498 Archived-At: Dear colleagues, Does anyone know whether every extensive and locally finitely presentable category fulfils the following condition: For every omega op-chain of coproduct injections i_n: A_n+1 -> A_n with all A_n finitely presentable some i_n is an isomorphism. We need this for investigating iterative monads in such categories, and we have not managed to prove it, nor to find a counterexample. Thanks, Jiri Adamek, Stefan Milius and Jiri Velebil xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx alternative e-mail address (in case reply key does not work): J.Adamek@tu-bs.de xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx