Yoneda lemma

== English == === Etymology === Lemma named after the Japanese mathematician Nobuo Yoneda (1930–1996). === Noun === Yoneda lemma (category theory) Given a category C {\displaystyle {\mathcal {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 {\displaystyle {\mathcal {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 {\displaystyle \alpha } from H to F is determined by what α A ( id A ) {\displaystyle \alpha _{A}({\mbox{id}}_{A})} is.) ==== Translations ==== === References ===