# Kerodon

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

Definition 5.3.7.1. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $(\infty ,2)$-categories. A functor from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$ is a morphism of simplicial sets $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ which carries thin $2$-simplices of $\operatorname{\mathcal{C}}$ to thin $2$-simplices of $\operatorname{\mathcal{D}}$.