Yoneda Embedding Theorem

Theorem
Let $C$ be a locally small category.

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

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

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