Kerodon

Remark 6.3.1.10. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. If $F$ exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to a collection of edges $W$, then, for every $\infty $-category $\operatorname{\mathcal{E}}$ and every morphism $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$, the composite map $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ carries each element of $W$ to an isomorphism in $\operatorname{\mathcal{E}}$. In particular, if $\operatorname{\mathcal{D}}$ itself is an $\infty $-category, then $F$ carries each element of $W$ to an isomorphism in $\operatorname{\mathcal{D}}$.