From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1876 Path: news.gmane.org!not-for-mail From: Philippe Gaucher Newsgroups: gmane.science.mathematics.categories Subject: preprint : The branching nerve of HDA and the Kan condition Date: Thu, 1 Mar 2001 15:00:57 +0100 (MET) Message-ID: <200103011400.PAA29145@irmast2.u-strasbg.fr> Reply-To: Philippe Gaucher NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018168 946 80.91.229.2 (29 Apr 2009 15:16:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:16:08 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Mar 1 14:47:52 2001 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f21I7Rg17252 for categories-list; Thu, 1 Mar 2001 14:07:27 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Content-MD5: m5MUpjIZPtWc83D5wO/PZQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.3.5 SunOS 5.7 sun4u sparc Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 1 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:1876 Archived-At: Title : The branching nerve of HDA and the Kan condition Abstract : We have already seen that in reasonable situations, i.e. when the path $\omega$-category associated to a higher dimensional automata (HDA) is an $\omega$-groupoid, only the globular nerve satisfies the Kan condition. Indeed for the branching and merging nerves, this condition generally does not hold. This drawback is overcome here by introducing two new nerves (the left and right globular nerves) satisfying the Kan condition in any reasonable situation and having conjecturally the same simplicial homology as the branching and merging nerves respectively for any $\omega$-category freely generated by a cubical set. Type : preprint Comment : 22 pages ; any comments are welcome. URLs : http://www-irma.u-strasbg.fr/~gaucher/fibrantcoin.ps.gz http://www-irma.u-strasbg.fr/~gaucher/fibrantcoin.pdf