Exponentiability of cartesian fibrations is not formal

Remark 23.8.2. The proposition is a genuine property of cartesian fibrations, not a formal property of arbitrary maps. For example, let \(\ell \colon [1]\to [2]\) be the long edge. The category \([2]\) is the pushout of the spine \[ [1]\sqcup _{[0]}[1], \] where the two copies of \([1]\) meet in the middle vertex. Pulling this pushout back along \(\ell \) gives two discrete vertices, whereas the pullback of \([2]\) along \(\ell \) is \([1]\). Thus \(-\times _{[2]}[1]\) does not preserve this pushout.