Categories of embeddings (Q1263665)

A categorical generalisation of the notion of domain, used in denotational semantics, is proposed. The generalized domain is a category of ``structures'' and embeddings which is closed under directed colimits and such that any ``structure'' is the directed colimit of its finite substructures. The category of all such categories is a cartesian closed category. Specialisation of the notion in the poset case gives new cartesian closed categories of domains. There is a close connection with Girard's model of polymorphism for \(F_{\omega}\).