Corollary 9.3.5.28. Let $\kappa $ be a small regular cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is $\kappa $-cocomplete and essentially small. Then the covariant Yoneda embedding
\[ h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \operatorname{Fun}^{\kappa -\operatorname{lex}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}) \]
exhibits $\operatorname{Fun}^{\kappa -\operatorname{lex}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ as an $\operatorname{Ind}_{\kappa }$-completion of $\operatorname{\mathcal{C}}$.