Variant 9.1.7.21. Let $\lambda $ and $\mu $ be uncountable regular cardinals satisfying $\lambda \trianglelefteq \mu $. Then every $\mu $-small $\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 $\mu $-small $\lambda $-directed partially ordered set and each $\operatorname{\mathcal{C}}_{\alpha }$ is a $\lambda $-small $\infty $-category. Moreover, if $\operatorname{\mathcal{C}}$ is filtered, we can arrange that each $\operatorname{\mathcal{C}}_{\alpha }$ is filtered.