Tukey morphisms between finite relations

This post is a link to https://arxiv.org/abs/2302.02772

With Rhett Barton and Paul Ellis.

Abstract: We investigate Tukey morphisms between binary relations, establishing several fundamental lemmas. We then specialize to finite binary relations, using computational methods to classify all binary relations with at most $6$ points in the domain and codomain up to bimorphism. Finally we give a construction of finite binary relations with arbitrary dominating number and dual dominating number.