Banaschewski defines and gives sufficient conditions on a category A and a subclass M of its monomorphisms under which M-injectivity well-behaves with respect to the notions such as M-absolute retract and M-essentialness. In this paper, taking A to be the category of S-posets over a posemigroup S and Mod to be the class of order dense regular monomorphisms, we study the behaviour of Mod-injectivity (also called order dense injectivity or od-injectivity).
