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/ ]