# Kerodon

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Exercise 5.5.6.5. Let $\operatorname{\mathcal{C}}$ be a category and let $\mathscr {F}$ be a functor from $\operatorname{\mathcal{C}}$ to the category of simplicial sets. Show that the comparison map $\theta : \int ^{\mathrm{s}}_{\operatorname{\mathcal{C}}}\mathscr {F} \rightarrow \int _{ \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) } \operatorname{N}_{\bullet }^{\operatorname{hc}}(\mathscr {F})$ of Construction 5.5.6.1 is a monomorphism of simplicial sets.