Kerodon

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

Remark 4.3.5.5. Let $f: K \rightarrow X$ be a morphism of simplicial sets. Then vertices of the slice simplicial set $X_{/f}$ are morphisms of simplicial sets $\overline{f}: K^{\triangleleft } \rightarrow X$ satisfying $\overline{f}|_{K} = f$. Similarly, vertices of the coslice simplicial set $X_{f/}$ are morphisms of simplicial sets $\overline{f}: K^{\triangleright } \rightarrow X$ satisfying $\overline{f}|_{K} = f$. Here $K^{\triangleleft }$ and $K^{\triangleright }$ denote the left and right cone of $K$ (Construction 4.3.3.22).