View example sentences and word forms for Cokernel.
Cokernel meaning
The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf. | The coequalizer of f and the zero morphism from X to Y, denoted operatorname cokerf. | The target of operatorname cokerf, denoted operatorname Cokerf.
Example sentences (8)
Analogously, one can show that the cokernel functors for abelian groups, vector spaces and modules are left adjoints.
It follows in particular that every cokernel is an epimorphism.
Kernels and cokernels Because the hom-sets in a preadditive category have zero morphisms, the notion of kernel and cokernel make sense.
Specifically: * AB1) Every morphism has a kernel and a cokernel.
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.
This means that every monomorphism is a kernel of some morphism, and every epimorphism is a cokernel of some morphism.
Unlike with products and coproducts, the kernel and cokernel of f are generally not equal in a preadditive category.
With an analogous construction, the cokernel of ƒ can be seen as an initial object of a suitable category.