A comonad for Grothendieck fibrations

Jacopo Emmenegger, Luca Mesiti, Giuseppe Rosolini +1

We prove that cloven Grothendieck fibrations over a fixed base $\ct{B}$ are the pseudo-coalgebras for a lax idempotent 2-comonad on $\ct{Cat}/\ct{B}$. We show this via an original…