Editing Ordered pair (section)

==Category theory==
[[File:CategoricalProduct-03.svg|thumb|[[Commutative diagram]] for the set product ''X''<sub>1</sub>×''X''<sub>2</sub>.]]
A category-theoretic [[Product (category theory)|product]] ''A'' × ''B'' in a [[category of sets]] represents the set of ordered pairs, with the first element coming from ''A'' and the second coming from ''B''. In this context the characteristic property above is a consequence of the [[universal property]] of the product and the fact that elements of a set ''X'' can be identified with morphisms from 1 (a one element set) to ''X''. While different objects may have the universal property, they are all [[naturally isomorphic]].