Example 7.4.2.9. Let $\operatorname{\mathcal{C}}$ be a simplicial set, let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}$ be the covariant transport representation of a left fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$, and let $\gamma : \mathscr {F} \rightarrow \mathscr {F}$ be the identity transformation. Then the identity map $\Gamma : \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{E}}$ is compatible with $\gamma $.
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