Corollary 8.5.4.11. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $f: K \rightarrow \operatorname{\mathcal{C}}$ be a morphism of simplicial sets. If $\operatorname{\mathcal{C}}$ is idempotent complete, then the slice and coslice $\infty $-categories $\operatorname{\mathcal{C}}_{/f}$ and $\operatorname{\mathcal{C}}_{f/}$ are idempotent complete.
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