# Kerodon

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Remark 5.5.6.15. The statement of Proposition 5.5.6.14 can be made more precise: Theorem 5.4.9.2 supplies an explicit $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched isomorphism from the identity functor $\operatorname{id}_{ \mathrm{h} \mathit{ \operatorname{QCat}} }$ to the composition

$\mathrm{h} \mathit{\operatorname{QCat}} \xrightarrow {\sim } \mathrm{h} \mathit{\operatorname{\mathcal{QC}}} \xrightarrow { \operatorname{hTr}_{ \operatorname{\mathcal{QC}}_{\operatorname{Obj}} / \operatorname{\mathcal{QC}}} } \mathrm{h} \mathit{\operatorname{QCat}},$

which carries each small $\infty$-category $\operatorname{\mathcal{C}}$ to the equivalence

$\theta _{\operatorname{\mathcal{C}}}: \operatorname{\mathcal{C}}\rightarrow \{ \operatorname{\mathcal{C}}\} \times _{\operatorname{\mathcal{QC}}} \operatorname{\mathcal{QC}}_{\operatorname{Obj}} = \operatorname{hTr}_{ \operatorname{\mathcal{QC}}_{\operatorname{Obj}} / \operatorname{\mathcal{QC}}}(\operatorname{\mathcal{C}})$

described in Remark 5.5.6.13.