Quotient set

Let be an equivalence relation on , and for each let denote its equivalence class. Then the quotient set is the set of all such equivalence classes naïve

with the natural projection

Universal property

The quotient set with canonical projection is characterized up to unique isomorphism by the universal property:

. If is a set a set and is a function with , then there exists a unique function so that , i.e.

Proof

This is fairly trivial to prove.

This notion is treated more generally by the Quotient object.