Kerodon

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Remark 6.2.4.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Every object $X \in \operatorname{\mathcal{C}}$ determines an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched functor $h_{X}: \mathrm{h} \mathit{\operatorname{\mathcal{C}}}^{\operatorname{op}} \rightarrow \mathrm{h} \mathit{\operatorname{Kan}}$, given on objects by the formula $h_{X}(C) = \underline{\operatorname{Hom}}_{\mathrm{h} \mathit{\operatorname{\mathcal{C}}}}( C, X) = \operatorname{Hom}_{\operatorname{\mathcal{C}}}(C,X)$. An arbitrary $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched functor $U: \mathrm{h} \mathit{\operatorname{\mathcal{C}}}^{\operatorname{op}} \rightarrow \mathrm{h} \mathit{\operatorname{Kan}}$ is represented by $X$ (in the sense of Definition 6.2.4.1) if and only if it is isomorphic to $h_{X}$.