In the general framework of a category with zero morphisms, the cokernel of *f* : *X*→*Y* (if it exists) is the morphism *g*: *Y*→*Z* such that the composition *gf* is the zero map from *X* to *Z* and *g* is universal for this property, i.e., any *h*: *Y*→*W* such that *hf* = 0 can be obtained by composing *g* with a unique map from *Z* to *W*.

This notion is dual to the kernels of category theory, hence the name.