# Kerodon

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Remark 8.5.5.3 (Isomorphism Invariance). Let $H: \operatorname{\mathcal{C}}\rightarrow \widehat{\operatorname{\mathcal{C}}}$ be a functor of $\infty$-categories, and let $H': \operatorname{\mathcal{C}}\rightarrow \widehat{\operatorname{\mathcal{C}}}$ be another functor which is isomorphic to $H$ (as an object of the $\infty$-category $\operatorname{Fun}( \operatorname{\mathcal{C}}, \widehat{\operatorname{\mathcal{C}}} )$). Then $H$ exhibits $\widehat{\operatorname{\mathcal{C}}}$ as an idempotent completion of $\operatorname{\mathcal{C}}$ if and only if $H'$ exhibits $\widehat{\operatorname{\mathcal{C}}}$ as an idempotent completion of $\operatorname{\mathcal{C}}$.