Domain theory, which studies directed complete partially ordered sets, was introduced by Scott in the 1970s as a foundation for programming semantics and provides an abstract model of computation, and has grown into a respected field on the borderline between mathematics and computer science. In this paper, we consider actions of a semigroup (monoid or group) on directed complete posets and study the algebraic notions of injectivity and retractness with respect to Scott closed embeddings in the categories so obtained.
کلید واژگان :
Dcpo, S-Dcpo, Scott closed embedding, injective object, retract.
