The existence of both kernels and cokernels gives a notion of image and coimage. We can define these as im f := ker coker f; coim f := coker ker f. That is, the image is the kernel of the cokernel, and the coimage is the cokernel of the kernel.
The existence of both kernels and cokernels gives a notion of image and coimage We can define these as im f := ker coker f; coim f := coker ker f. That is, the image is the kernel of the cokernel, and the coimage is the cokernel of the kernel.