For any functor F: C → Set and object A, natural transformations Hom_C(A, −) ⇒ F are in bijection with F(A). 'An object is determined by how other objects see it.' Central result of category theory.
For any functor F: C → Set and object A, natural transformations Hom_C(A, −) ⇒ F are in bijection with F(A). 'An object is determined by how other objects see it.' Central result of category theory.