# Kerodon

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

Exercise 4.5.8.5. Let $X$ and $Y$ be simplicial sets. Show that the comparison map $c_{X,Y}: X \diamond Y \rightarrow X \star Y$ of Notation 4.5.8.3 is an epimorphism of simplicial sets: that is, it is surjective at the level of $n$-simplices for each $n \geq 0$.