Kerodon

Example 9.5.6.18 (Truncated Objects). Let $\operatorname{\mathcal{C}}$ be a presentable $\infty $-category, let $n$ be an integer, and let $\operatorname{\mathcal{C}}_{\leq n}$ denote the full subcategory of $\operatorname{\mathcal{C}}$ spanned by the $n$-truncated objects. Then $\operatorname{\mathcal{C}}_{\leq n}$ is a Bousfield localization of $\operatorname{\mathcal{C}}$. This is a special case of Proposition 9.5.6.15, since the full subcategory $\operatorname{\mathcal{C}}_{\leq n}$ is accessibly embedded (Corollary 9.4.8.14) and closed under limits (Corollary 7.3.8.7).