Kernel (set Theory) - Quotients

Quotients

Like any equivalence relation, the kernel can be modded out to form a quotient set, and the quotient set is the partition:

This quotient set is called the coimage of the function, and denoted (or a variation). The coimage is naturally isomorphic (in the set-theoretic sense of a bijection) to the image, ; specifically, the equivalence class of in (which is an element of ) corresponds to in (which is an element of ).