Homomorphism-homogeneous relational structures

Abstract

We study relational structures (especially graphs and posets) which satisfy the analogue of homogeneity but for homomorphisms rather than isomorphisms. The picture is rather different. Our main results are partial characterizations of countable graphs and posets with this property; an analogue of Fraïssé's theorem; and representations of monoids as endomorphism monoids of such structures. © 2006 Cambridge University Press.