Category of abelian groups

In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category: indeed, every small abelian category can be embedded in Ab.

The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the surjective group homomorphisms, and the isomorphisms are the bijective group homomorphisms.