Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 9.2.5.27. Let $\operatorname{\mathcal{C}}$ be an essentially small $\infty $-category which admits finite colimits. Then the covariant Yoneda embedding

\[ h_{\bullet }: \operatorname{\mathcal{C}}\rightarrow \operatorname{Fun}^{\operatorname{lex}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}}) \]

exhibits $\operatorname{Fun}^{\operatorname{lex}}( \operatorname{\mathcal{C}}^{\operatorname{op}}, \operatorname{\mathcal{S}})$ as an $\operatorname{Ind}$-completion of $\operatorname{\mathcal{C}}$.

Proof. Apply Corollary 9.2.5.26 in the special case $\kappa = \aleph _0$. $\square$