Yoneda Embedding Theorem

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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.


Proof