# Kerodon

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

Definition 4.5.6.1. Let $\operatorname{\mathcal{C}}$ be a category and let $\alpha : \mathscr {F} \rightarrow \mathscr {G}$ be a natural transformation between diagrams $\mathscr {F}, \mathscr {G}: \operatorname{\mathcal{C}}\rightarrow \operatorname{Set_{\Delta }}$. We say that $\alpha$ is a levelwise categorical equivalence if, for every object $C \in \operatorname{\mathcal{C}}$, the induced map $\alpha _{C}: \mathscr {F}(C) \rightarrow \mathscr {G}(C)$ is a categorical equivalence of simplicial sets.