Definition 6.3.3.1. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. We will say that $F$ is a localization functor if there exists a collection of morphisms $W$ in $\operatorname{\mathcal{C}}$ such that $F$ exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$.
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