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.