Some more notions of homomorphism–homogeneity

We extend the notion of ‘homomorphism–homogeneity’ to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism–homogeneity, giving several examples. We also give further details on related work reported in Lockett and Truss (2012) about the endomorphisms of chains and generic endomorphisms of trees.