Tukey Morphisms Between Finite Binary Relations

Let A = ( A − , A + , A ) and B = ( B − , B + , B ) be relations. A morphism is a pair of maps φ − : B − → A − and φ + : A + → B + such that for all b ∈ B − and a ∈ A + , φ − ( b ) Aa ⟹ bBφ + ( a ). We study the existence of morphisms between finite relations. The ultimate goal is to identify the conditions under which morphisms exist. In this thesis we present some progress towards that goal. We use computation to verify the results for small finite relations.