Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 3.1.2.4. Let $i: A_{} \hookrightarrow B_{}$ be an inner anodyne morphism of simplicial sets (Definition 1.5.6.4). Then $i$ is anodyne. The converse is false in general. For example, the horn inclusions $\Lambda ^{n}_0 \hookrightarrow \Delta ^ n$ and $\Lambda ^{n}_{n} \hookrightarrow \Delta ^ n$ are anodyne (for $n > 0$), but are not inner anodyne.