Is there a reference for the following infinity category fact? I have been scouring HTT and the Barwick school papers. @DenisNardin?
If F:C\to Cat is a functor, then the associated cocartesian fibration is also a cartesian fibration if and only if F(f) has a right adjoint for all morphisms f.
If F:C\to Cat is a functor, then the associated cocartesian fibration is also a cartesian fibration if and only if F(f) has a right adjoint for all morphisms f.