Definition 2.4.1.6. Let $\operatorname{\mathcal{C}}_{\bullet }$ be a simplicial category, and let $f,g: X \rightarrow Y$ be two morphisms in the underlying category $\operatorname{\mathcal{C}}= \operatorname{\mathcal{C}}_0$ having the same source and target. A homotopy from $f$ to $g$ is an edge $h \in \operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{1}$ satisfying $d^{1}_1(h) = f$ and $d^{1}_0(h) = g$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$