From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3055 Path: news.gmane.org!not-for-mail From: Marco Grandis Newsgroups: gmane.science.mathematics.categories Subject: Re: Undirected graphs citation Date: Wed, 1 Mar 2006 09:41:45 +0100 Message-ID: References: <440335A6.3050806@cs.stanford.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v746.2) Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019069 7066 80.91.229.2 (29 Apr 2009 15:31:09 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:31:09 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 1 09:16:06 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 01 Mar 2006 09:16:06 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FER6i-0000Ek-Cr for categories-list@mta.ca; Wed, 01 Mar 2006 09:11:08 -0400 In-Reply-To: <440335A6.3050806@cs.stanford.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-IMAPbase: 1144781894 151 X-Keywords: X-UID: 1 Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:3055 Archived-At: Vaughan Pratt asked about: > undirected graphs ... as presheaves on the full subcategory 1 and > 2 of Set? It is the 2-truncation of "symmetric simplicial sets" as presheaves on finite cardinals, cf (*). Curiously, symmetric simplicial sets have been rarely considered. Even if simplicial complexes (well-known!) are a symmetric notion and have a natural embedding in symmetric simplicial sets. While simplicial sets are a directed notion, used as an undirected one in classical Algebraic Topology. (*) M. Grandis, Finite sets and symmetric simplicial sets, Theory Appl. Categ. 8 (2001), No. 8, 244-252. Marco Grandis