The following is the definition of an Abelian category according to Barry Mitchell (1965).
The following theorem from ref.[1] is also relevant as it relates key properties of Abelian
categories:
“The following statements are equivalent:
- 𝒜 is an Abelian category;
- 𝒜 has kernels, cokernels, finite products, finite coproducts, and is both
normal and comormal;
- 𝒜 has pushouts and pullbacks and is both normal and conormal”.
References
[1] Barry Mitchell. Theory of Categories, Academic Press: New York and London, 1965,
(Theorem 20.1 on p.33).
