Remark 5.6.6.12. Let $\operatorname{\mathcal{C}}$ be an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched category. Then an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched functor $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \mathrm{h} \mathit{\operatorname{Kan}}$ is corepresentable by an object $X \in \operatorname{\mathcal{C}}$ if and only if it is isomorphic (as an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched functor) to the functor
\[ \operatorname{\mathcal{C}}\rightarrow \mathrm{h} \mathit{\operatorname{Kan}} \quad \quad Y \mapsto \underline{\operatorname{Hom}}_{\operatorname{\mathcal{C}}}(X,Y). \]