# Kerodon

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Example 7.4.3.4. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let ${\bf 1}$ denote the cone point of $\operatorname{\mathcal{C}}^{\triangleright }$. Using Example 5.2.3.18, we see that the tautological map $V: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow (\Delta ^{0})^{\triangleright } \simeq \Delta ^1$ is a cocartesian fibration. If $\overline{U}: \overline{\operatorname{\mathcal{E}}} \rightarrow \operatorname{\mathcal{C}}^{\triangleright }$ is another cocartesian fibration, then the $\infty$-categories $\operatorname{\mathcal{E}}= \operatorname{\mathcal{C}}\times _{\operatorname{\mathcal{C}}^{\triangleright }} \overline{\operatorname{\mathcal{E}}}$ and $\overline{\operatorname{\mathcal{E}}}_{ {\bf 1} } = \{ {\bf 1} \} \times _{ \operatorname{\mathcal{C}}^{\triangleright } } \overline{\operatorname{\mathcal{E}}}$ can be identified with the fibers of the composite map

$(V \circ \overline{U} ): \overline{\operatorname{\mathcal{E}}} \rightarrow \Delta ^1,$

which is also a cocartesian fibration (Proposition 5.1.4.13). In this case, the covariant refraction diagram $\mathrm{Rf}: \operatorname{\mathcal{E}}\rightarrow \overline{\operatorname{\mathcal{E}}}_{ {\bf 1} }$ of Proposition 7.4.3.3 is given by covariant transport for the cocartesian fibration $V \circ \overline{U}$ (along the nondegenerate edge of $\Delta ^1$).