Yoneda Embedding Theorem

Theorem
Let $C$ be a locally small category.

Let $\mathbf{Set}$ be the category of sets.

Let $[C^{\operatorname{op}}, \mathbf{Set}]$ be the contravariant functor category.

Then the Yoneda embedding $h_- : C \to [C^{\operatorname{op}}, \mathbf{Set}]$ is a fully faithful embedding.