# Canonical map

A standard form of canonical map involves some function mapping a set ${\displaystyle X}$ to the set ${\displaystyle X/R}$ (${\displaystyle X}$ modulo ${\displaystyle R}$), where ${\displaystyle R}$ is an equivalence relation on ${\displaystyle X}$.[1] A closely related notion is a structure map or structure morphism; the map or morphism that comes with the given structure on the object. These are also sometimes called canonical maps.