In: Jensen, K.: Lecture Notes in Computer Science, Vol. 616; 13th International Conference on Application and Theory of Petri Nets 1992, Sheffield, UK, pages 76-92. Springer-Verlag, June 1992.
Abstract: Category theory has been applied to Petri nets in two distinct ways. The first approach is to define a category whose objects are Petri nets and whose morphisms represent the refinement of one net by another. The second approach is to define a category whose objects are themselves categories representing the possible computations of the net. We establish a close connection between these two approaches by exhibiting a reflection between a category of nets and a category of behaviour categories.The morphisms in our categories have an appealing computational interpretation in terms of simulation, which is closely related to the notion of simulation in process algebra.