Kerodon

Proposition 8.5.5.4. Let $\operatorname{\mathcal{C}}$ be an essentially small $\infty $-category and let $h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \operatorname{Fun}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ be a covariant Yoneda embedding for $\operatorname{\mathcal{C}}$ (Definition 8.3.3.9). Then the functor $h_{\bullet }$ exhibits $\operatorname{Fun}^{\mathrm{atm}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ as an idempotent completion of $\operatorname{\mathcal{C}}$.