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Yoneda lemma

Related Terms:

category natural transformation representable functor functor isomorphism

Noun

Definition: 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 𝛼_A( mbox id_A) is.)

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