In mathematics, a canonical map, also called a natural map, is a map or morphism between objects that arises naturally from the definition or the construction of the objects.
Often, it is a map which preserves the widest amount of structure.
A closely related notion is a structure map or structure morphism; the map or morphism that comes with the given structure on the object.
In some contexts, it might be necessary to address an issue of choices of canonical maps or canonical isomorphisms; for a typical example, see prestack.
For a discussion of the problem of defining a canonical map see Kevin Buzzard's talk at the 2022 Grothendieck conference.