Essential monomorphism

In mathematics, specifically category theory, an essential monomorphism is a monomorphism "f" in a category "C" such that for a morphism "g" in "C", the morphism formula_1 is a monomorphism only when "g" is a monomorphism. Essential monomorphisms in a category of modules are those whose image is an essential submodule of the codomain. An injective hull of an object "X" is an essential monomorphism from "X" to an injective object.