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.

It provides a way to represent functors as natural transformations.

It allows us to prove a variety of results in category theory.

It is used in other areas of mathematics, such as algebraic topology and algebraic geometry.

All of the above.

A functor that embeds a category into the category of presheaves on that category.

A functor that embeds a category into the category of functors from that category to Set.

A functor that embeds a category into the category of natural transformations from the constant functor to the identity functor on that category.

None of the above.

The Yoneda embedding is a special case of Yoneda's Lemma.

Yoneda's Lemma can be used to prove the Yoneda embedding.

The Yoneda embedding and Yoneda's Lemma are independent results.

None of the above.

It can be used to prove the existence of limits and colimits in a category.

It can be used to prove the uniqueness of limits and colimits up to isomorphism.

It can be used to construct the category of presheaves on a category.

All of the above.