Warning 8.5.4.28. The collection of idempotent complete $\infty $-categories is not closed under the formation of colimits in $\operatorname{\mathcal{QC}}$. (In fact, every $\infty $-category $\operatorname{\mathcal{C}}$ can be realized as a colimit of standard simplices $\Delta ^ n$, which are idempotent complete $\infty $-categories: see Proposition 
.) However, we will see in ยง8.5.9 that the collection of idempotent complete $\infty $-categories is closed under filtered colimits: see Corollary 8.5.9.10.
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