Article · Wikipedia archive · Last revised Jun 13, 2026

Essential monomorphism

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. 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.

Last revised
Jun 13, 2026
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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 f i {\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

References

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.