In set theory, a **projection** is one of two closely related types of functions or operations, namely:

- A set-theoretic operation typified by the
^{th}projection map, written that takes an element of the Cartesian product to the value^{[1]} - A function that sends an element to its equivalence class under a specified equivalence relation
^{[2]}or, equivalently, a surjection from a set to another set.^{[3]}The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image. The result of the mapping is written as when is understood, or written as when it is necessary to make explicit.