Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Remark 3.1.6.3. Let $f: X_{} \rightarrow Y_{}$ be a morphism of simplicial sets. The condition that $f$ is a homotopy equivalence depends only on the homotopy class $[f] \in \pi _0( \operatorname{Fun}(X_{}, Y_{} ) )$. Moreover, if $f$ is a homotopy equivalence, then its homotopy inverse $g: Y_{} \rightarrow X_{}$ is determined uniquely up to homotopy.