Exercise 5.5.2.2. Let $\operatorname{\mathcal{C}}$ be a simplicial category containing an object $X$. Show that the simplicial categories $\operatorname{\mathcal{C}}_{/X}$ and $\operatorname{\mathcal{C}}_{X/}$ of Construction 5.5.2.1 are well-defined (that is, the composition law of Construction 5.5.2.1 is unital and associative).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$