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The statement of the Yoneda lemma has a straightforward generalization from categories to (∞,1)-categories.
-Yoneda embedding
Let be an (∞,1)-category and be the corresponding (∞,1)-category of (∞,1)-presheaves. Then the canonical (∞,1)-functor
-Yoneda theorem
For a small -category and an -functor, the composite
is equivalent to .
This appears as HTT Lemma 5.5.2.1.
The statement is a direct consequence of the sSet-enriched Yoneda lemma by using the fact that the (infinity,1)-category of (infinity,1)-presheaves is modeled by the enriched functor category with regarded as a simplicially enriched category and using the global model structure on simplicial presheaves.
Published statements appear in
as indicated above.
See also the discussion on MathOverflow.