From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9370 Path: news.gmane.org!.POSTED!not-for-mail From: Patrik Eklund Newsgroups: gmane.science.mathematics.categories Subject: Re: Functionally complete/universal basis for graph homomorphisms? Date: Sat, 30 Sep 2017 11:18:28 +0300 Message-ID: References: Reply-To: Patrik Eklund NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII; format=flowed Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1506794017 21309 195.159.176.226 (30 Sep 2017 17:53:37 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sat, 30 Sep 2017 17:53:37 +0000 (UTC) Cc: categories To: Vaughan Pratt Original-X-From: majordomo@mlist.mta.ca Sat Sep 30 19:53:32 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 1dyLxD-0004vY-K3 for gsmc-categories@m.gmane.org; Sat, 30 Sep 2017 19:53:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46720) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1dyLxw-0001cB-D4; Sat, 30 Sep 2017 14:54:16 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1dyLw8-0001T6-JC for categories-list@mlist.mta.ca; Sat, 30 Sep 2017 14:52:24 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9370 Archived-At: Dear Vaughan, I will under the CATLIST and at this point not reply more in detail, but let me just now say that your "categories are not algebraic in sets, at least they are algebraic in graphs, which in turn are algebraic in sets" is within the realm of "algebraic categories". My "Categorizing automata is hard enough as we see through Budach, Ehrig, Goguen, Manes, Adamek, etc." is in the realm of "categorical algebra" and monoidal categories. So with graphs understood as being useful also for representing terms with "vertices in trees seen as operator names", like it is done e.g. in tree automata, monoidal categories as underlying categories of term monads is another view and machinery as compared to dealing with the category of graphs as an algebraic category ("categories are algebraic in graphs"). Best, Patrik On 2017-09-28 08:50, Vaughan Pratt wrote: > 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/ ]