# Kerodon

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Proposition 4.7.2.1 (Existence of Localizations). Let $\operatorname{\mathcal{C}}$ be a simplicial set and let $W$ be a collection of edges of $\operatorname{\mathcal{C}}$. Then there exists an $\infty$-category $\operatorname{\mathcal{D}}$ and a morphism of simplicial sets $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$.

Proof of Proposition 4.7.2.1. Apply Proposition 4.7.2.5 in the special case $\operatorname{\mathcal{D}}= \Delta ^{0}$. $\square$