Kerodon

Example 8.5.8.12. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. For every integer $n \geq 0$, the skeleton $\operatorname{sk}_{n}(\operatorname{\mathcal{C}})$ satisfies condition $(\ast _ m)$ of Lemma 8.5.8.11 for $0 \leq m \leq n$. We can therefore choose an inner anodyne morphism $\iota : \operatorname{sk}_{n}(\operatorname{\mathcal{C}}) \hookrightarrow \operatorname{\mathcal{E}}$, where $\operatorname{\mathcal{E}}$ is an $\infty $-category and $f$ is bijective on simplices of dimension $< n$.