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Example Let $\operatorname{\mathcal{QC}}$ denote the $\infty $-category of (small) $\infty $-categories. Then $\operatorname{\mathcal{QC}}$ is idempotent complete. More generally, for every uncountable cardinal $\kappa $, the $\infty $-category $\operatorname{\mathcal{QC}}^{< \kappa }$ of $\kappa $-small $\infty $-categories is idempotent complete. To prove this, we can use Propositions and to reduce to the case where $\kappa $ has uncountable cofinality. In this case, the $\infty $-category $\operatorname{\mathcal{QC}}^{< \kappa }$ admits sequential colimits (Example, so the desired result follows from Corollary