* Term for edges between graph homomorphisms?
@ 2017-03-16 16:58 Mike Stay
0 siblings, 0 replies; 2+ messages in thread
From: Mike Stay @ 2017-03-16 16:58 UTC (permalink / raw)
To: categories
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/ ]
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* Re: Term for edges between graph homomorphisms?
@ 2017-03-17 18:03 RONALD BROWN
0 siblings, 0 replies; 2+ messages in thread
From: RONALD BROWN @ 2017-03-17 18:03 UTC (permalink / raw)
To: Mike Stay, categories
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/ ]
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