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Kerodon

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

Corollary 8.7.3.13. Let $\mathbb {K}$ be a collection of small simplicial sets and let $\operatorname{\mathcal{C}}$ be a locally small $\infty $-category. Then the $\mathbb {K}$-cocompletion of $\operatorname{\mathcal{C}}$ is also locally small.

Proof. Apply Proposition 8.7.3.11 in the special case where $\lambda = \operatorname{\textnormal{\cjRL {t}}}$ is a strongly inaccessible cardinal (see Remark 8.7.3.11). $\square$