Yoneda Lemma

A statement in category theory that for any locally small category C, object A in C, and functor F: C^op → Set, there is a natural bijection between natural transformations Hom_C(-,A) ⇒ F and elements of the set F(A); this bijection is natural in both A and F and yields the Yoneda embedding of C into the functor category [C^op,Set].

A fundamental result in category theory that identifies the elements of a presheaf at an object with natural transformations from the representable functor Hom(−, A) to that presheaf, thereby representing objects of a category by their functors of points and establishing a fully faithful embedding of the category into a presheaf category.