PlanetPhysics/Abelian Category
The following is the definition of an Abelian category according to Barry Mitchell (1965).
Definition
An Abelian category is an [[../CategoricalSequence/|exact]] [[../DenseSubcategory/|additive category]] with finite products.
The following [[../Formula/|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.