Proposition 9.5.4.7 (Cocontinuous Limits of Presentable $\infty $-Categories). Suppose we are given a small diagram $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{QC}}_{\leq \Omega }$ satisfying the following conditions:
For every vertex $C \in \operatorname{\mathcal{C}}$, the $\infty $-category $\mathscr {F}(C)$ is presentable.
For every edge $e: C \rightarrow C'$ of $\operatorname{\mathcal{C}}$, the functor $\mathscr {F}(e): \mathscr {F}(C) \rightarrow \mathscr {F}(C')$ is cocontinuous.
Then the limit $\varprojlim ( \mathscr {F} )$ is also a presentable $\infty $-category.