From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3089 Path: news.gmane.org!not-for-mail From: Jiri Rosicky Newsgroups: gmane.science.mathematics.categories Subject: symmetric simplicial sets Date: Mon, 13 Mar 2006 15:17:37 +0100 Message-ID: <20060313141737.GA24776@queen.math.muni.cz> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-2 X-Trace: ger.gmane.org 1241019088 7193 80.91.229.2 (29 Apr 2009 15:31:28 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:31:28 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Mar 13 18:54:59 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 13 Mar 2006 18:54:59 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FIvuv-0001Dk-Ml for categories-list@mta.ca; Mon, 13 Mar 2006 18:53:33 -0400 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 35 Original-Lines: 15 Xref: news.gmane.org gmane.science.mathematics.categories:3089 Archived-At: One advantage of symmetric simplicial sets is that their model category structure is determined, cf. (*), by taking cofibrations as monomorphisms. It means that the classical homotopy category Ho (of CW-complexes) can be obtained just from the category S of symmetric simplicial sets (without any additional data). Simplicial sets do not have this property (it was also observed by J. H. Smith). In (*), we have used this property of S to give an elementary proof of an important result of D. Dugger saying that Ho is a free homotopy theory over a point. (*) J. Rosicky and W. Tholen, Left-determined model categories and universal homotopy theories, TAMS 355 (2003), 3611-3623.