# Kerodon

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

Remark 4.5.1.18 (Two-out-of-Three). Let $F: \operatorname{\mathcal{C}}_{} \rightarrow \operatorname{\mathcal{D}}_{}$ and $G: \operatorname{\mathcal{D}}_{} \rightarrow \operatorname{\mathcal{E}}_{}$ be functors between $\infty$-categories. If any two of the functors $F$, $G$, and $G \circ F$ is an equivalence of $\infty$-categories, then so is the third. In particular, the collection of equivalences is closed under composition.