Kerodon

Example 9.4.8.10. Let $\operatorname{\mathcal{S}}$ denote the $\infty $-category of spaces (Construction 3.1.6.1), let $n$ be an integer, and let $\operatorname{\mathcal{S}}^{\leq n}$ denote the full subcategory of $\operatorname{\mathcal{S}}$ spanned by the $n$-truncated Kan complexes. Then the full subcategory $\operatorname{\mathcal{S}}^{\leq n} \subseteq \operatorname{\mathcal{S}}$ is replete (Corollary 3.5.7.8), reflective (Example 6.2.2.12), and closed under small filtered colimits (Variant 9.1.9.3). Applying Proposition 9.4.8.9, we conclude that $\operatorname{\mathcal{S}}^{\leq n}$ is an accessibly embedded full subcategory of $\operatorname{\mathcal{S}}$. See Corollary 9.4.9.14 for a more general statement.