Fixed-point constructions in order-enriched categories

AbstractThe fixed-point construction of Scott, giving a continuous lattice solution of equations X ≅ T(X) where T is an endofunctor on the category of continuous lattices, is extended to categories enriched by partial orderings on the morphism sets. The result allows data structures to be realized not only in the category of continuous lattices, but also in the category of complete lattices, in the category of complete partial orders, or in any of several related categories of partial orders