Variant 5.2.8.11 (Enriched Homotopy Transport: Left Fibrations). Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a left fibration of $\infty $-categories. Applying Construction 5.2.8.9, we obtain an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched functor
\[ \operatorname{hTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}: \mathrm{h} \mathit{\operatorname{\mathcal{C}}} \rightarrow \mathrm{h} \mathit{\operatorname{Kan}}, \]
given on objects by the formula $\operatorname{hTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}( C ) = \{ C \} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$.