In mathematics, specifically category theory, an essential monomorphism is a monomorphism i in an abelian category C such that for a morphism f in C, the composition ${\displaystyle fi}$ is a monomorphism only when f is a monomorphism.^[1] Essential monomorphisms in a category of modules are those whose image is an essential submodule of the codomain. An injective hull of an object A is an essential monomorphism from A to an injective object.^[1]