Cokernel

Summary

In a category with zero morphisms, the cokernel of a morphism $f$ is the universal morphism $q$ with $q \circ f = 0$. It is the coequalizer of $f$ and the zero morphism, and the notion dual to the kernel. For modules, the cokernel of $f \colon X \to Y$ is the quotient map $Y \to Y / f(X)$. The cokernel measures how far a morphism is from being surjective.