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
This theorem requires a proof. In particular: use Yoneda Lemma for Contravariant Functors You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |