From: RONALD BROWN <ronnie.profbrown@btinternet.com>
To: Mike Stay <metaweta@gmail.com>, categories@mta.ca
Subject: Re: Term for edges between graph homomorphisms?
Date: Fri, 17 Mar 2017 18:03:18 +0000 (GMT) [thread overview]
Message-ID: <E1cpwkL-0003ZC-LP@mlist.mta.ca> (raw)
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/ ]
next reply other threads:[~2017-03-17 18:03 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2017-03-17 18:03 RONALD BROWN [this message]
-- strict thread matches above, loose matches on Subject: below --
2017-03-16 16:58 Mike Stay
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