# Kerodon

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Definition 6.3.3.11. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty$-categories. We say that $F$ is a reflective localization if it exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$, where $W$ is a localizing collection of morphisms of $\operatorname{\mathcal{C}}$. We say that $F$ is a coreflective localization if it exhibits $\operatorname{\mathcal{D}}$ as a localization of $\operatorname{\mathcal{C}}$ with respect to $W$, where $W$ is a colocalizing collection of morphisms of $\operatorname{\mathcal{C}}$.