Preadditive Category - Special Cases

Special Cases

Most of these special cases of preadditive categories have all been mentioned above, but they're gathered here for reference.

  • A ring is a preadditive category with exactly one object.
  • An additive category is a preadditive category with all finite biproducts.
  • A pre-Abelian category is an additive category with all kernels and cokernels.
  • An Abelian category is a pre-Abelian category such that every monomorphism and epimorphism is normal.

The preadditive categories most commonly studied are in fact Abelian categories; for example, Ab is an Abelian category.

Read more about this topic:  Preadditive Category

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