Remark 9.5.4.9. In the situation of Proposition 9.5.4.7, suppose that $\operatorname{\mathcal{D}}$ is a cocomplete $\infty $-category. Then a functor $T: \operatorname{\mathcal{D}}\rightarrow \varprojlim (\mathscr {F})$ is cocontinuous if and only if, for each $C \in \operatorname{\mathcal{C}}$, the composite functor $\operatorname{\mathcal{D}}\xrightarrow {T} \varprojlim (\mathscr {F}) \rightarrow \mathscr {F}(C)$ is cocontinuous. See Proposition 7.6.6.24.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$