Example 8.5.4.4. Let $X$ be a Kan complex. Since the simplicial set $\operatorname{N}_{\bullet }(\operatorname{Idem})$ is weakly contractible (Remark 8.5.3.4), every morphism of simplicial sets $\operatorname{N}_{\bullet }( \operatorname{Idem}) \rightarrow X$ is homotopic to a constant map. It follows that $X$ is idempotent complete when viewed as an $\infty $-category.
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