Bisimulations of enrichments

In this paper we show that classical notions from automata theory such as simulation and bisimulation can be lifted to the context of enriched categories. The usual properties of bisimulation are nearly all preserved in this new context. The class of enriched functors that correspond to functionnal bisimulations surjective on objects is investigated and appears to be “very close” to be open in the sense of Joyal and Moerdijk [4]. Seeing the change of base techniques as a convenient means to define process refinement/abstractions we give sufficient conditions for the change of base categories to preserve bisimularity. We apply these concepts to Betti’s generalized automata, categorical transition systems, and other exotic categories.