Yoneda's Lemma

For any category C and any object X in C, there is a natural isomorphism between the functor category C/X and the category of functors from C to Set.

For any category C and any object X in C, there is a natural isomorphism between the functor category C/X and the category of natural transformations from the constant functor X to the identity functor on C.

For any category C and any object X in C, there is a natural isomorphism between the functor category C/X and the category of natural transformations from the identity functor on C to the constant functor X.

For any category C and any object X in C, there is a natural isomorphism between the functor category C/X and the category of functors from C to Set that preserve finite limits.