From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7073 Path: news.gmane.org!not-for-mail From: Andrew Salch Newsgroups: gmane.science.mathematics.categories Subject: monads on model categories Date: Sat, 26 Nov 2011 19:49:07 -0500 (EST) Message-ID: Reply-To: Andrew Salch NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: dough.gmane.org 1322404113 23789 80.91.229.12 (27 Nov 2011 14:28:33 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 27 Nov 2011 14:28:33 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Nov 27 15:28:29 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RUfiX-0004tP-27 for gsmc-categories@m.gmane.org; Sun, 27 Nov 2011 15:28:29 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:52968) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RUfhi-000630-0l; Sun, 27 Nov 2011 10:27:38 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RUfhg-0002BG-F8 for categories-list@mlist.mta.ca; Sun, 27 Nov 2011 10:27:36 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7073 Archived-At: Suppose C is a category and T is a monad on C. One knows that one can factor T into a composite GF, where F,G are an adjoint pair of functors, and in fact one knows that there are two universal ways to do this, a Kleisli/initial construction and an Eilenberg-Moore/terminal construction. Now suppose C is a model category and T is a monad on C which preserves weak equivalences. One would like to know that T factors as GF, where F,G are a Quillen pair. Is this always possible and does one have Kleisli-like and Eilenberg-Moore-like constructions with appropriate universal properties? I am sure people have worked on these questions before; where can I read about this? Thanks, Andrew S. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]