# Kerodon

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Example 8.5.4.19. 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 8.5.4.6 and 8.5.1.12 to reduce to the case where $\kappa$ has uncountable cofinality. In this case, the $\infty$-category $\operatorname{\mathcal{QC}}^{< \kappa }$ admits sequential colimits (Example 7.6.7.7), so the desired result follows from Corollary 8.5.4.17.