# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$

Example 4.5.1.13. Let $f: X \rightarrow Y$ be a morphism of Kan complexes. Then $f$ is a homotopy equivalence if and only if it is an equivalence of $\infty$-categories (see Remark 4.5.1.3). In this case, a morphism $g: Y \rightarrow X$ is an inverse to $f$ (in the sense of Remark 4.5.1.10) if and only if it is a homotopy inverse to $f$ (in the sense of Definition 3.1.5.1).