On categorical approach to reaction systems

Abstract

In every matured theory, there is a need to investigate possible relationships between considered objects. To address this issue, it is natural to relate a category with given model of computing. Thanks to such approach, many properties are unified and simplified. In this paper, we investigate how category theory can be used to give a faithful semantics for reaction systems. In particular, we propose and discuss possible approaches to the problem of defining morphisms between reaction systems. We provide the definition of morphism that keeps the behaviour of the original reaction system. Especially, some equivalences of reaction systems are reflected in terms of morphisms. For this purpose we expressed isomorphisms and sections in term of transition systems. Moreover, the accelerating morphism defined in the last section gives a new approach for including time in reaction systems.