From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2507 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: question about lambda-filtered colimits Date: Mon, 1 Dec 2003 13:45:04 +0100 Organization: PPS Message-ID: <200312011345.04078.gaucher@pps.jussieu.fr> Reply-To: gaucher@pps.jussieu.fr 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 1241018711 4487 80.91.229.2 (29 Apr 2009 15:25:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:25:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Dec 1 09:16:54 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 01 Dec 2003 09:16:54 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1AQnoC-00034p-00 for categories-list@mta.ca; Mon, 01 Dec 2003 09:09:48 -0400 User-Agent: KMail/1.5 Content-Disposition: inline X-Antivirus: scanned by sophie at shiva.jussieu.fr Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 1 Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:2507 Archived-At: Dear category theorists I would be interested in knowing a proof of the following fact (due to J. Smith): "In a combinatorial model category M (i.e. a locally presentable cofibrantly generated model category), there are functorial factorizations of a map into a trivial cofibration followed by a fibration which preserve lambda-filtered colimits for sufficiently large regular cardinals lambda. The same is true for the factorizations as a cofibration followed by a trivial fibration." As far as I know about the proof, it suffices to apply the small object argument step-by-step and then to use some property of lambda-filtered colimits. The only property I know close to the problem is that a lambda-filtered colimits of lambda-presentable objects is lambda-presentable. But the underlying diagram of a pushout is not lambda-filtered. So I dont understand... Thanks in advance. pg.