Example 8.5.4.2. Let $\operatorname{\mathcal{C}}$ be a category. If $\operatorname{\mathcal{C}}$ admits equalizers (or coequalizers), then the $\infty $-category $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is idempotent complete (this is a restatement of Corollary 8.5.2.6). In particular, if $\operatorname{\mathcal{C}}$ admits finite limits or finite colimits, then $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ is idempotent complete.
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