Example 8.5.4.20. Let $\operatorname{\mathcal{S}}$ denote the $\infty $-category of spaces. Then $\operatorname{\mathcal{S}}$ is idempotent complete. More generally, for every uncountable cardinal $\kappa $, the $\infty $-category $\operatorname{\mathcal{S}}^{< \kappa }$ of $\kappa $-small spaces is idempotent complete. This follows from Example 8.5.4.19 and Proposition 8.5.4.6, since the full subcategory $\operatorname{\mathcal{S}}^{< \kappa } \subseteq \operatorname{\mathcal{QC}}^{< \kappa }$ is closed under the formation of retracts (Remark 8.5.1.16).
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