Definition of Cokernels. Meaning of Cokernels. Synonyms of Cokernels

- codomain of f by the image of f. The dimension of the cokernel is called the corank of f. Cokernels are dual to the kernels of category theory, hence the...
- specifically because of the existence of kernels and cokernels. Although kernels and cokernels are special kinds of equalisers and coequalisers, a pre-abelian...
- in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototypical example...
- which all biproducts, kernels, and cokernels exist is called pre-abelian. Further facts about kernels and cokernels in preadditive categories that are...
- with the inclusion homomorphism i : K → A. The same is true for cokernels; the cokernel of f is the quotient group C = B / f(A) together with the natural...
- zero object. Then there is an exact sequence relating the kernels and cokernels of a, b, and c: ker ⁡ a   ⟶   ker ⁡ b   ⟶   ker ⁡ c   ⟶ d   coker ⁡ a...
- "F turns cokernels into cokernels"); G is left-exact if and only if A→B→C→0 exact implies 0→G(C)→G(B)→G(A) exact (i.e. if "G turns cokernels into kernels");...
- left-exact but not necessarily right-exact: cokernels of morphisms in A do not in general correspond to the cokernels of the corresponding morphisms in Mod-R...
- of R-Mod in such a way that kernels and cokernels computed in A correspond to the ordinary kernels and cokernels computed in R-Mod. Such an equivalence...
- categories without requiring that morphisms actually possess kernels and cokernels, which is necessary for the usual definition of such a sequence. An exact...