From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1638 Path: news.gmane.org!not-for-mail From: "Dominic Verity" Newsgroups: gmane.science.mathematics.categories Subject: RE: characterisation of nerve of omega-categories Date: Sat, 23 Sep 2000 11:26:09 +1000 Message-ID: <000201c024fd$40b58e60$6df16f89@pascal.mpce.mq.edu.au> References: <200009221607.SAA11033@irmast2.u-strasbg.fr> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241017984 32190 80.91.229.2 (29 Apr 2009 15:13:04 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:13:04 +0000 (UTC) To: "Philippe Gaucher" , Original-X-From: rrosebru@mta.ca Mon Sep 25 00:50:08 2000 -0300 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id XAA24962 for categories-list; Sun, 24 Sep 2000 23:39:32 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from zent.mta.ca (zent.mta.ca [138.73.101.4]) by mailserv.mta.ca (8.9.3/8.9.3) with SMTP id VAA02829 for ; Fri, 22 Sep 2000 21:27:02 -0300 (ADT) X-Received: FROM macadam.mpce.mq.edu.au BY zent.mta.ca ; Fri Sep 22 21:28:55 2000 -0300 X-Received: from hera.mpce.mq.edu.au (hera.mpce.mq.edu.au [137.111.219.13]) by macadam.mpce.mq.edu.au (8.8.8/8.8.8) with ESMTP id LAA17672; Sat, 23 Sep 2000 11:26:52 +1100 (EST) X-Received: from pascal (mpce-remote31.mpce.mq.edu.au [137.111.241.109]) by hera.mpce.mq.edu.au (8.9.3+Sun/8.9.3) with SMTP id LAA18478; Sat, 23 Sep 2000 11:26:50 +1100 (EST) X-Priority: 3 (Normal) X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook 8.5, Build 4.71.2173.0 Importance: Normal In-Reply-To: <200009221607.SAA11033@irmast2.u-strasbg.fr> X-MimeOLE: Produced By Microsoft MimeOLE V4.72.3110.3 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 24 Original-Lines: 63 Xref: news.gmane.org gmane.science.mathematics.categories:1638 Archived-At: Hi Philippe, The answer to your question is that, to my knowledge, the characterisation of the nerves of n-categories currently only exists in conjectural form in the literature. In particular, a full description of this conjecture is given in the paper: "The Algebra of Oriented Simplexes" by Ross Street (JPAA 49 (1987) pp 283-335) and an associated note "Fillers for Nerves" (I forget the precise reference) which proves the necessity of this characterisation. This actual conjecture is originally due to John Roberts - it does involve simplicial sets enriched with a distinguished set of "hollow" or "thin" simplices and appropriate "admissible" horn filler conditions with respect to these thin simplices. Roberts calls these structures "complicial sets". I presented a proof of this conjecture to a conference at UC Berkeley (MSRI) in 1993 (I think) and also in a number of seminars given at Bangor in Wales and at the Sydney Category Seminar, but unfortunately never published the result, due to a subsequent career change (I became an investment banker). Roberts' original conjecture as described by Street does indeed hold - in fact a slightly weaker result may be proved which only involves fillers for "inner" horns. More recently, I have taken some time away from the world of finance and am currently working on writing up my results in this area - which I hope to make available over the next few months. All the very best Dominic Verity Macquarie University Sydney, Australia > -----Original Message----- > From: cat-dist@mta.ca [mailto:cat-dist@mta.ca]On Behalf Of Philippe > Gaucher > Sent: Saturday, 23 September 2000 2:07 > To: categories@mta.ca > Subject: categories: characterisation of nerve of omega-categories > > > Dear all, > > I don't remember where I could find a characterization for > a simplicial set to be the simplicial nerve of some strict > globular omega-category ? I think that the characterization > is that the simplicial set must be given with a structure > of thin elements satisfying some axioms like the filling of > horners and thin horners. Could you send me a reference please ? > > Thank you in advance. pg. > > >