Unifying theories in different institutions(*)

Abstract

We investigate functorial relationships between the categories of theories in different institutions, namely adjunctions, as a means of translating between the different specification spaces that they provide. We show that there is a canonical way in which adjunctions between the categories of signatures can be lifted to the categories of theories. This lifting is associated with a duality between the concepts of institution map and institution morphism. Finally, we make an attempt at generalising these results to institution semi-morphisms that can be presented by an inference system.