Kerodon

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

Corollary 9.1.7.4. Let $\lambda $ be an uncountable regular cardinal. Then every filtered $\infty $-category $\operatorname{\mathcal{C}}$ can be realized as the colimit of some diagram

\[ A \rightarrow \operatorname{Set_{\Delta }}\quad \quad (\alpha \in A) \mapsto \operatorname{\mathcal{C}}_{\alpha }, \]

where $(A, \leq )$ is a $\lambda $-directed partially ordered set and each $\operatorname{\mathcal{C}}_{\alpha }$ is a $\lambda $-small filtered $\infty $-category. Moreover, $\operatorname{\mathcal{C}}$ is also a colimit of the diagram $\{ \operatorname{\mathcal{C}}_{\alpha } \} _{\alpha \in A}$ in the $\infty $-category $\operatorname{\mathcal{QC}}$.