Remark 9.5.6.3 (Transitivity). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories. Assume that $\operatorname{\mathcal{C}}$ is presentable and that $F$ is a Bousfield localization functor (so that $\operatorname{\mathcal{D}}$ is also presentable). Then $G$ is a Bousfield localization functor if and only if the composition $(G \circ F): \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{E}}$ is a Bousfield localization functor.
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