2-Yoneda lemma
In mathematics, especially category theory, the 2-Yoneda lemma is a generalization of the Yoneda lemma to 2-categories. Precisely, given a contravariant pseudofunctor F {\displaystyle F} on a category C, it says: for each object x {\displaystyle x} in C, the natural functor (evaluation at the identity) Hom _ ( h x , F ) → F ( x ) {\displaystyle {\underline {\operatorname {Hom} }}(h_{x},F)\to F(x)} is an equivalence of categories, where Hom _ ( − , − ) {\displaystyle {\underline {\operatorname {Hom} }}(-,-)} denotes (roughly) the category of natural transformations between pseudofunctors on C and h x = Hom ( − , x ) {\displaystyle h_{x}=\operatorname {Hom} (-,x)} .