Behavioural equivalences for coalgebras with unobservable moves
Categories enriched over the category of CPOs with binary joins and continuous maps are studied as a host for endomorphism saturation. A construction to embed CPO-enriched categories into a category admitting saturation is presented and shown to be equivalent to any such embedding. Weak behavioural equivalences are defined in terms of homomorphisms-of-endomorphisms (cf. kernel bisimulation) from a saturated system. Implications of left (resp. right) distributivity of binary joins w.r.t. weak and strong behavioural equivalences are investigated. The framework is shown to instantiate to several existing weak behavioural equivalences and to be applicable to complex settings like presheaves.
weak behavioural equivalences process calculi coalgebraic semantics saturation semantics