PlanetPhysics/Abelian Category

The following is the definition of an Abelian category according to Barry Mitchell (1965).

Definition

An Abelian category is an exact additive category with finite products.

The following theorem from ref.^[1] is also relevant as it relates key properties of Abelian categories:

The following statements are equivalent:

${\mathcal {A}}$ is an Abelian category;

${\mathcal {A}}$ has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;

${\mathcal {A}}$ has pushouts and pullbacks and is both normal and conormal.

All Sources

^[1]

References

↑ ^1.0 ^1.1 Barry Mitchell. Theory of Categories , Academic Press: New York and London, 1965, (Theorem 20.1 on p.33).

[BM65-1] 1.0 ^1.1 Barry Mitchell. Theory of Categories , Academic Press: New York and London, 1965, (Theorem 20.1 on p.33).

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