Corollary 8.5.5.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category which can be realized as the limit of a small diagram $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{QC}}$. Suppose that, for each vertex $D \in \operatorname{\mathcal{D}}$, the $\infty $-category $\mathscr {F}(D)$ is idempotent complete. Then $\operatorname{\mathcal{C}}$ is idempotent complete.
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