# Kerodon

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

Remark 8.1.0.2. Let $\operatorname{\mathcal{C}}$ be a category. Then the construction $(f: X \rightarrow Y) \mapsto (X,Y)$ determines a forgetful functor $\lambda : \operatorname{Tw}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{\mathcal{C}}^{\operatorname{op}} \times \operatorname{\mathcal{C}}$. Moreover, $\lambda$ is a left covering functor, in the sense of Definition 4.2.3.1.