From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9158 Path: news.gmane.org!.POSTED!not-for-mail From: RONALD BROWN Newsgroups: gmane.science.mathematics.categories Subject: Re: Term for edges between graph homomorphisms? Date: Fri, 17 Mar 2017 18:03:18 +0000 (GMT) Message-ID: Reply-To: RONALD BROWN NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit X-Trace: blaine.gmane.org 1490014279 925 195.159.176.226 (20 Mar 2017 12:51:19 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Mon, 20 Mar 2017 12:51:19 +0000 (UTC) To: Mike Stay , categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Mon Mar 20 13:51:14 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 1cpwmI-0008Ag-FG for gsmc-categories@m.gmane.org; Mon, 20 Mar 2017 13:51:14 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:58445) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cpwkz-0007RF-RT; Mon, 20 Mar 2017 09:49:53 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cpwkL-0003ZC-LP for categories-list@mlist.mta.ca; Mon, 20 Mar 2017 09:49:13 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9158 Archived-At: Mike, You might find the following paper relevant: R. Brown, I. Morris, J. Shrimpton and C.D. Wensley, `Graphs of Morphisms of Graphs', Electronic Journal of Combinatorics, A1 of Volume 15(1), 2008. 1-28. However we do not seem to have given a name to the arrows of GPH(B,C) occurring in Gph(A \time B, C) \cong Gph(A, GPH(B,C)). Ronnie ----Original message---- >From : metaweta@gmail.com Date : 16/03/2017 - 16:58 (GMTST) To : categories@mta.ca Subject : categories: Term for edges between graph homomorphisms? If we define a graph to be a tuple (E, V, s: E -> V, t: E -> V), then the category Gph of graphs and graph homomorphisms is cartesian closed (in fact, a topos). For any pair of graphs G, G', there is a "hom graph" whose vertices are graph homomorphisms from G to G' and whose edges are things I've been calling "graph shifts". A graph shift S between two graph homomorphisms F, F':G -> G' assigns to each vertex g in G an edge S(g) in G' from F(g) to F'(g). Is there a more common term for a "graph shift"? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]