# Kerodon

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Example 6.3.1.6. Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ denote its homotopy category (Definition 1.2.5.1). Let $W$ be a collection of edges of $\operatorname{\mathcal{C}}$, let $[W]$ denote the collection of morphisms in $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ which belong to the image of $W$, and let $F: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \operatorname{\mathcal{D}}$ be a functor of ordinary categories which exhibits $\operatorname{\mathcal{D}}$ as a strict localization of $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ with respect to $[W]$ (Definition 6.3.0.1). If $\operatorname{\mathcal{E}}$ is an ordinary category, then we have a canonical isomorphism of simplicial sets

$\operatorname{Fun}( \operatorname{\mathcal{C}}[W^{-1}], \operatorname{N}_{\bullet }(\operatorname{\mathcal{E}}) ) \simeq \operatorname{N}_{\bullet }( \operatorname{Fun}(\operatorname{\mathcal{D}}, \operatorname{\mathcal{E}}) ).$