Domain Theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. It was introduced in the 1970s by Scott 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 take domains as ordered algebraic structures and consider the actions of a partially ordered monoid which is itself a domain, on them. To study algebraic notions, in particular injectivity and flatness, in the categories so obtained, one needs to know the different kinds of monomorphisms, their properties and the relations between them. This is what we are going to discuss in this paper.