Yoneda lemma

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The Yoneda lemma is a fundamental result in category theory, a branch of mathematics. It is an abstract result on functors of the type morphisms into a fixed object. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It also generalizes the information-preserving relation between a term and its continuation-passing style transformation from programming language theory. It allows the embedding of any locally small category into a category of functors (contravariant set-valued functors) defined on that category. It also clarifies how the embedded category of representable functors and their natural transformations relates to the other objects in the larger functor category. It is an important tool that underlies several modern developments in algebraic geometry and representation theory. It is named after Nobuo Yoneda.

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