Map (mathematics)

In mathematics, a map or mapping is a function in its general sense.^[1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.^[2]

The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial.^[3][4] In category theory, a map may refer to a morphism.^[2] The term transformation can be used interchangeably,^[2] but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.