Definition 9.5.6.1. Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is a Bousfield localization functor if the $\infty $-category $\operatorname{\mathcal{D}}$ is presentable and $F$ admits a fully faithful right adjoint.
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