cokernel

Noun

Meaning

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.

Anagrams

Examples

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

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