From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9157 Path: news.gmane.org!.POSTED!not-for-mail From: Mike Stay Newsgroups: gmane.science.mathematics.categories Subject: Term for edges between graph homomorphisms? Date: Thu, 16 Mar 2017 10:58:00 -0600 Message-ID: Reply-To: Mike Stay NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: blaine.gmane.org 1489771217 17944 195.159.176.226 (17 Mar 2017 17:20:17 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Fri, 17 Mar 2017 17:20:17 +0000 (UTC) To: categories Original-X-From: majordomo@mlist.mta.ca Fri Mar 17 18:20:13 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 1covXr-0003lU-4i for gsmc-categories@m.gmane.org; Fri, 17 Mar 2017 18:20:07 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:57801) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1covWn-0003Pk-AX; Fri, 17 Mar 2017 14:19:01 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1covW8-0000Ap-FD for categories-list@mlist.mta.ca; Fri, 17 Mar 2017 14:18:20 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9157 Archived-At: 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/ ]