Noun
cokernel (plural cokernels)
(category theory) For a category with zero morphisms: the coequalizer between a given morphism and the zero morphism which is parallel to that given morphism.
Analogously, one can show that the cokernel functors for abelian groups, vector spaces and modules are left adjoints. Source: Internet
It follows in particular that every cokernel is an epimorphism. Source: Internet
Kernels and cokernels Because the hom-sets in a preadditive category have zero morphisms, the notion of kernel and cokernel make sense. Source: Internet
Specifically: * AB1) Every morphism has a kernel and a cokernel. Source: Internet
That is, if f: A → B is a morphism in a preadditive category, then the kernel of f is the equaliser of f and the zero morphism from A to B, while the cokernel of f is the coequaliser of f and this zero morphism. Source: Internet
This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism. Source: Internet