Actions of a monoid or a group on a set have always been of interest to mathematicians and computer scientists. On the other hand, 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, combining the above two notions, we consider actions of a semigroup (monoid or group) on compact reversible directed complete posets and study the algebraic notion of retractness, which is tightly connected to the study of injectivity, with respect to monomorphisms and embeddings in the category so obtained.
کلید واژگان :Action of a monoid, directed complete poset, absolute retract, injective object.
ارزش ریالی : 300000 ریال
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