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

Notation (Slicing over Vertices). Let $X$ be a simplicial set containing a vertex $x$, and let $f_{x}: \Delta ^{0} \rightarrow X$ be the map carrying the unique vertex of $\Delta ^0$ to $x$. We will generally abuse notation by not distinguishing between the vertex $x$ and the morphism $f_ x$. For example, we will denote the slice simplicial set $X_{/f_ x}$ by $X_{/x}$, and the coslice simplicial set $X_{f_ x/}$ by $X_{x/}$.