Corollary 9.2.4.24. Let $\kappa $ be a small regular cardinal, let $\operatorname{\mathcal{C}}$ be a locally small $\infty $-category, and let $\widehat{\operatorname{\mathcal{C}}} \subseteq \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ be the full subcategory spanned by the $\kappa $-flat functors $\mathscr {F}: \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{S}}$ which are left Kan extended from an essentially small full subcategory of $\operatorname{\mathcal{C}}$. Then the covariant Yoneda embedding
\[ h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \widehat{\operatorname{\mathcal{C}}} \subseteq \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}) \]
exhibits $\widehat{\operatorname{\mathcal{C}}}$ as an $\operatorname{Ind}_{\kappa }$-completion of $\operatorname{\mathcal{C}}$.