Yoneda lemma

English

Etymology

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

Noun

1. Template:Lb 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 $\alpha$ from H to F is determined by what ${\alpha }_A({\text{id}}_A)$ is.)

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