Category theory MOC

Abelian category

An abelian category is a preäbelian category such that every monomorphism is a kernel and every epimorphism is a cokernel. cat Thus in particular an abelian category is enriched over Category of abelian groups and admits finite biproducts.

The prototypical example is Category of abelian groups, or more generally Category of left modules for any ring . The Freyd-Mitchell theorem gives a sense in which all abelian categories are categories of modules.

Properties

• Exact functor on abelian categories

Subtypes

• Spectral category
  • Semisimple category
    • Fusion category

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