Example 3.1.7.13. Let $n \geq 0$ be an integer and let $X$ be a simplicial set which satisfies the following condition:
- $(\ast )$
For $0 < m \leq n$, every horn $\Lambda ^{m}_{i} \rightarrow X$ can be extended to an $m$-simplex of $X$.
Applying Variant 3.1.7.12 to the projection map $X \rightarrow \Delta ^0$, we conclude that $X$ admits an anodyne map $f: X \hookrightarrow Q$ which is bijective on $k$-simplices for $k < n$, where $Q$ is a Kan complex.