cokernel

This term is a specialized technical expression used almost exclusively within the domains of linear algebra, category theory, and homological algebra. It describes the "remainder" of a codomain after the image of a morphism has been factored out, serving as a dual concept to the kernel.

In practical application, the cokernel is used to measure how far a linear map is from being surjective. If the cokernel is trivial (zero), the map is surjective. Because it is a formal mathematical object, it is used in highly formal academic and professional contexts and has no colloquial or metaphorical usage.