Homotopy inverse
= Homotopy inverse
If $g\circ f\simeq\operatorname{id}_X$ and $f\circ g\simeq\operatorname{id}_Y$, then $g$ is a homotopy inverse of $f$ and conversely.
= Homotopy equivalent
{synonym}
= Homotopy inverse
If $g\circ f\simeq\operatorname{id}_X$ and $f\circ g\simeq\operatorname{id}_Y$, then $g$ is a homotopy inverse of $f$ and conversely.
= Homotopy equivalent
{synonym}