PlanetPhysics/Abelian Category

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

Definition

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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:

  1. is an Abelian category;
  2. has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;
  3. has pushouts and pullbacks and is both normal and conormal.

All Sources

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[1]

References

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