Example 8.5.1.34. In the situation of Lemma 8.5.1.33, suppose that $S = [n] \setminus \{ j\} $ for some $0 \leq j \leq n$. Then $K$ is the horn $\Lambda ^{n}_{j} \subseteq \Delta ^ n$. The hypothesis of Lemma 8.5.1.33 guarantees that $K$ is an inner horn, so that the inclusion map $K \hookrightarrow \Delta ^ n$ is inner anodyne by definition.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$