Coopcartesian Morphism

A coopcartesian morphism in $\mathcal{E}\to\mathcal{B}$ is a Cartesian Morphism in the Fibrewise Opposite of the Total Opposite of $\mathcal{E}$. Note that this requires $\mathcal{E}$ to be a Cartesian Fibration, which is somewhat unsatisfying.

This comes from Pavlovic, II.3.2, though he calls such fibrations trifibrations, and only considers them in the context of additional Bifibrational structure.