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Effaceable functor

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In mathematics, an effaceable functor is an additive functor F between abelian categories C and D for which, for each object A in C, there exists a monomorphism u: A \to M, for some M, such that F(u). [1]

5 relations: Abelian category, Delta-functor, Grothendieck's Tôhoku paper, Monomorphism, Preadditive category.

Abelian category

In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties.

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In homological algebra, a δ-functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of derived functors.

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Grothendieck's Tôhoku paper

The article "Sur quelques points d'algèbre homologique" by Alexander Grothendieck, now often referred to as the Tôhoku paper, was published in 1957 in the Tôhoku Mathematical Journal.

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In the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism.

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Preadditive category

In mathematics, specifically in category theory, a preadditive category is a category that is enriched over the monoidal category of abelian groups.

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[1] https://en.wikipedia.org/wiki/Effaceable_functor

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