In category theory, a natural numbers object is an object equipped with a distinguished global element z and a distinguished endomorphism s such that the iterated compositions sn ∘ z yield the natural numbers, and it satisfies the universal property that for any other object with a distinguished global element z' and endomorphism s', there is a unique morphism φ with φ ∘ z = z' and φ ∘ s = s' ∘ φ.
In category theory, a natural numbers object is an object equipped with a distinguished global element z and a distinguished endomorphism s such that the iterated compositions sn ∘ z yield the natural numbers, and it satisfies the universal property that for any other object with a distinguished global element z' and endomorphism s', there is a unique morphism φ with φ ∘ z = z' and φ ∘ s = s' ∘ φ.
圏論において、自然数対象とは、終対象からの指定された点 z と指定された自己射 s を備え、s^n ∘ z の反復が自然数に対応し、さらに任意の他の対象に指定された点 z' と自己射 s' が与えられるときに z を z' に写し s と可換な一意の射 φ が存在するという普遍性を満たす対象である。
