Remark 5.6.8.8. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. It follows from Lemmas 5.6.8.6 and 5.6.8.7 that $\operatorname{TW}( \operatorname{\mathcal{E}}/ \operatorname{\mathcal{C}})$ can be identified with the full subcategory of the Kan complex
\[ \operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{QC}})^{\simeq } \times _{ \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}})^{\simeq } } \operatorname{Fun}( \operatorname{\mathcal{E}}, \operatorname{\mathcal{QC}}_{\operatorname{Obj}} )^{\simeq } \]
spanned by those pairs $(\mathscr {F}, \widetilde{\mathscr {F}} )$ which witness $\mathscr {F}$ as a covariant transport representation for $U$.