A Theory of Recursive Domains with Applications to Concurrency

We develop a 2-categorical theory for recursively defined domains. In particular, we generalise the traditional approach based on order-theoretic structures to category-theoretic ones. A motivation for this development is the need of a domain theory for concurrency, with an account of bisimulation. Indeed, the leading examples throughout the paper are provided by recursively defined presheaf models for concurrent process calculi. Further, we use the framework to study (open-map) bisimulation.