Essential monomorphism
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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 is a monomorphism only when f is a monomorphism.{{cite book|last=Hashimoto|first=Mitsuyasu|title=Auslander-Buchweitz Approximations of Equivariant Modules|url=https://books.google.com/books?id=OOBkgAmsWnsC|page=19|isbn=9780521796965|publisher=Cambridge University Press|via=Google Books|publication-date=November 2, 2000|access-date=February 3, 2024}} 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.