Kerodon

Proposition 9.2.4.5. Let $\operatorname{\mathcal{C}}$ be an essentially small $\infty $-category. Then the convariant Yoneda embedding $h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ factors through $\operatorname{Fun}^{\flat }( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$, and exhibits $\operatorname{Fun}^{\flat }( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ as an $\operatorname{Ind}$-completion of $\operatorname{\mathcal{C}}$ (in the sense of Definition 9.2.1.1).