University of Wales, Bangor - Mathematics Preprints 2004
Category Theory & Homotopy Theory
04.19
BROWN, R., MORRIS, I., SHRIMPTON, J. & WENSLEY, C.D.
Graphs of morphisms of graphs
Abstract:
From the categorical viewpoint, the endomorphisms of a graph
should not only be composable, giving a monoid structure,
but should also have a notion of adjacency,
so that the set of endomorphisms is both a monoid and a graph.
We extend Shrimpton's investigations on the morphism-digraphs of
reflexive digraphs to the undirected case by using an equivalence between
a category of reflexive, undirected graphs and the category of
reflexive, directed graphs with reversal.
