📚 noun • entry_id 51888
Yoneda lemma
Meanings (ES + gloss)
lema de Yoneda
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.)
As a corollary of the Yoneda lemma, given a pair of contravariant hom functors #92;mbox#123;Hom#125;(-,A) and #92;mbox#123;Hom#125;(-,B), then any natural transformation #92;alpha…
• Yoneda Lemma: Nat(Hom(A,–), F) ≅ F(A) ∴ Nat(Hom(A,–), Hom(B,–)) ≅ Hom(B,A) ∴ A ≅ B iff Hom(A,–) ≅ Hom(B,–) i.e. A is isomorphic to B if and only if A's network of relations is is…
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