In set theory, a projection is one of two closely related types of functions or operations, namely:
- A set-theoretic operation typified by the jth projection map, written , that takes an element of the Cartesian product to the value .
- A function that sends an element x to its equivalence class under a specified equivalence relation E, or, equivalently, a surjection from a set to another set. 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 [x] when E is understood, or written as [x]E when it is necessary to make E explicit.