An **Abelian category** is a type of category in the field of category theory that has particular properties making it a suitable framework for doing homological algebra. The notion was introduced by the mathematician Alexander Grothendieck in the context of algebraic geometry, but it has applications across various areas of mathematics.
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An abelian category is an additive category with all kernels and cokernels in which every monomorphism and epimorphism is normal.