Remark 1.5.1.6. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. If $f: X \rightarrow Y$ is a morphism in $\operatorname{\mathcal{C}}$ and $g: Y \rightarrow X$ is a homotopy inverse to $f$, then $F(g)$ is a homotopy inverse to $F(f)$. In particular, if $f$ is an isomorphism in $\operatorname{\mathcal{C}}$, then $F(f)$ is also an isomorphism in $\operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$