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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 ${\displaystyle fi}$ is a monomorphism only when f 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 A is an essential monomorphism from A to an injective object.

References

1. ^ Hashimoto, Mitsuyasu (November 2, 2000). Auslander-Buchweitz Approximations of Equivariant Modules. Cambridge University Press. p. 19. ISBN 9780521796965. Retrieved February 3, 2024 – via Google Books.

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