Yoneda lemma

Lemma named after the Japanese mathematician Nobuo Yoneda (1930–1996).

1(category theory) Given a category 𝒞 with an object A, let H be a hom functor represented by A, and let F be any functor (not necessarily representable) from 𝒞 to Sets, then there is a natural isomorphism between Nat(H,F), the set of natural transformations from H to F, and the set F(A). (Any natural transformation α from H to F is determined by what αA(idA) is.)