Enriched Categories for Local and Interaction Calculi

The construction of models for distributed computations plays a very important role in designing and developing parallel computing systems. Various algebraic approaches have been proposed in the past as, for instance, the communicating computing agents of [Mil80], [BeK85], and [BHR84]. In our work we propose a general method for defining the categorical models for classes of algebras of distributed computing agents. If the static and dynamic operations [Mil80] of the algebras enjoy suitable properties, we can construct enriched categories which are models of distributed computations, including also the case of concurrent finite automata which cooperate via protocols. The construction is uniform with respect to the particular algebra one may wish to consider.