Concise Graphs and Functional Bisimulations

We investigate the conditions under which least bisimulations exist with respect to set inclusion. In particular, we describe a natural way to remove redundant pairs from a given bisimulation. We then introduce the conciseness property on process graphs, which characterizes the existence of least bisimulations under the aforementioned method. Subsequently, we consider the category of process graphs and functional bisimulations. This category has all coequalizers. Binary products and coproducts can be constructed with some further assumptions. Moreover, the full subcategory of concise graphs is a reflective subcategory.