Proposition 23.2.4. Let \(p\colon E\to C\) be a cocartesian fibration classified by a functor \(F\colon C\to \Cat _{\infty }\), and let \(I\) be a small \(\infty \)-category. The composite \[ C\xrightarrow {F}\Cat _{\infty }\xrightarrow {\Fun (I,-)}\Cat _{\infty } \] is classified by the cocartesian fibration \[ C\times _{\Fun (I,C)}\Fun (I,E)\longrightarrow C, \] where the map \(\Fun (I,E)\to \Fun (I,C)\) is induced by \(p\) and the map from \(C\) sends an object to its constant \(I\)-diagram.
Proof. See Reference ? of [Cisinski et al. (2026)]. □
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