Green’s relations in some categories of strong graph homomorphisms

Abstract

The immediate purpose of this paper is to show how Li’s characterization of Green’s relations on monoids of strong endomorphisms of graphs [8] is related to earlier work of Klasa [5] on categories. Li’s results are thus extended to some categories of strong graph homomorphisms with more than one object, and a finiteness requirement is weakened. A further purpose is to extend Klasa’s results in such a way as to better reflect the factorization properties of interesting concrete categories.