ON CATEGORICAL PROPERTIES OF S-POSET REGULAR MONOMORPHISMS

In category theory, monomorphisms frequently are too weak to represent substructures. The notion of regular monomorphism, which equalizes some parallel pair of morphisms, is usually coincide with natural subobjects in many categories such as S-posets (posets on which the actions of a pomonoid S preserve the order). In this talk, we study some categorical properties of (regular) monomorphisms in the categories of posets and S-posets. we also characterize all absolutely retract posets (with respect to all monomorphisms) and then prove that posets have enough absolutely retracts.