A master’s thesis by Rhett Barton, Summer 2021

Abstract: Let $\mathbf{A} = (A_{-},A_{+},A)$ and $\mathbf{B} = (B_{-},B_{+},B)$ be relations. A morphism is a pair of maps $\varphi_{-}:B_{-} \to A_{-}$ and $\varphi_{+}:A_{+} \to B_{+}$ such that for all $b \in B_{-}$ and $a \in A_{+}$, $\varphi_{-}(b)Aa \implies bB\varphi_{+}(a)$. 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.