Corollary 9.5.5.13. Let $\kappa \trianglelefteq \lambda $ be regular cardinals, let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is $\lambda $-cocomplete and $\kappa $-compactly generated, and let $\operatorname{\mathcal{D}}$ be an $\infty $-category which is $(\kappa ,\lambda )$-cocomplete. Then the restriction functor
\[ \operatorname{Fun}^{\lambda -\mathrm{cocont}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \rightarrow \operatorname{Fun}^{ \kappa -\mathrm{cocont} }( \operatorname{\mathcal{C}}_{< \kappa }, \operatorname{\mathcal{D}}) \]
is an equivalence of $\infty $-categories.