From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1797 Path: news.gmane.org!not-for-mail From: "Walter Tholen" Newsgroups: gmane.science.mathematics.categories Subject: preprint: Lax factorization algebras Date: Mon, 22 Jan 2001 10:43:39 -0500 Message-ID: <1010122104339.ZM218104@pascal.math.yorku.ca> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018111 531 80.91.229.2 (29 Apr 2009 15:15:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:15:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Jan 22 13:06:44 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f0MGBvC01240 for categories-list; Mon, 22 Jan 2001 12:11:57 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Z-Mail (4.0.1 13Jan97) Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 28 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:1797 Archived-At: The ps-file of the following paper is available via my website at www.math.yorku.ca/Who/Faculty/Tholen/research.html Please do not hesitate contacting me in case of difficulty. Walter. -------------------------------------------------------------------------- "Lax factorization algebras" Jiri Rosicky' and Walter Tholen Abstract: It is shown that many weak factorization systems appearing in functorial Quillen model categories, including all those that are cofibrantly generated, come with a rich computational structure, defined by a certain lax algebra with respect to the "squaring monad" on CAT. This structure largely facilitates natural choices for left or right liftings once certain basic natural choices have been made. The use of lax homomorphisms of such lax algebras is also discussed, with focus on "lax freeness".