Warning 1.4.6.9. Let $f: X \rightarrow Y$ be a morphism in an $\infty $-category $\operatorname{\mathcal{C}}$, and suppose that $g,h: Y \rightarrow X$ are left homotopy inverses to $f$. If $f$ does not admit a right homotopy inverse, then $g$ and $h$ need not be homotopic.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$