Kerodon

Example 9.6.8.7. Let $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$ denote the $\infty $-category whose objects are presentable $\infty $-categories and whose morphisms are cocontinuous functors (Construction 9.5.3.1). Let $S_{L}$ be the collection of morphisms in $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$ which Bousfield localization functors (Definition 9.5.6.1) and let $S_{R}$ be the collection of morphisms of $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$ given by conservative functors. Then the pair $(S_ L, S_ R)$ is a factorization system on $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$. See Example 9.6.6.8 and Proposition 9.5.7.10.