PlanetPhysics/Abelian Category
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The following is the definition of an Abelian category according to Barry Mitchell (1965).
Definition
[edit | edit source]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:
- is an Abelian category;
- has kernels, cokernels, finite products, finite coproducts, and is both normal and comormal;
- has pushouts and pullbacks and is both normal and conormal.