From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9368 Path: news.gmane.org!.POSTED!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Functionally complete/universal basis for graph homomorphisms? Date: Wed, 27 Sep 2017 22:50:25 -0700 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1506622385 28012 195.159.176.226 (28 Sep 2017 18:13:05 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Thu, 28 Sep 2017 18:13:05 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Thu Sep 28 20:13:01 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1dxdIt-0006Ue-8N for gsmc-categories@m.gmane.org; Thu, 28 Sep 2017 20:12:55 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46245) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dxdKC-0007eB-Va; Thu, 28 Sep 2017 15:14:16 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dxdIN-0007xx-KT for categories-list@mlist.mta.ca; Thu, 28 Sep 2017 15:12:23 -0300 In-Reply-To: Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9368 Archived-At: On 09/26/17 9:28 PM, Patrik Eklund wrote: > The category of graphs may also need revision. Defining a graph as > mapping an edge to a pair of vertices hides arities and invites to > defining paths. Nevertheless, vertices in trees are seen as operator > names. Even though categories are not algebraic in sets, at least they are algebraic in graphs, which in turn are algebraic in sets. While I would have little or no quarrel with any revision of "the" category of graphs that preserved this fundamental relation between categories and sets, if the revision you have in mind does not then I would expect at least some of us here would be very interested in why you consider your contemplated revision an improvement. Vaughan Pratt [For admin and other information see: http://www.mta.ca/~cat-dist/ ]