Kerodon

Remark 7.4.5.7. In the situation of Definition 7.4.5.6, suppose that $\mathrm{Rf}: \operatorname{\mathcal{E}}\rightarrow \overline{\operatorname{\mathcal{E}}}_{ {\bf 1} }$ is a covariant refraction diagram. Then, for every vertex $C \in \operatorname{\mathcal{C}}$, the restriction $\mathrm{Rf}|_{ \operatorname{\mathcal{E}}_{C} }: \operatorname{\mathcal{E}}_{C} \rightarrow \overline{\operatorname{\mathcal{E}}}_{ {\bf 1} }$ is given by covariant transport along the unique edge $e_{C}: C \rightarrow {\bf 1}$ of $\operatorname{\mathcal{C}}^{\triangleright }$, in the sense of Definition 5.2.2.4.