Warning 4.7.8.12. In the situation of Proposition 4.7.8.10, the map $\operatorname{\mathcal{C}}\rightarrow \operatorname{cosk}_{n+1}(\operatorname{\mathcal{C}})$ is generally not an inner fibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Warning 4.7.8.12. In the situation of Proposition 4.7.8.10, the map $\operatorname{\mathcal{C}}\rightarrow \operatorname{cosk}_{n+1}(\operatorname{\mathcal{C}})$ is generally not an inner fibration.