Fibrewise Terminal Objects

A Cartesian Fibration $\mathcal{E}\rightarrowtriangle\mathcal{B}$ is said to have fibrewise terminal objects if the Fibred Functor

Properties

• A Cartesian Fibration $\mathcal{E}$ has fibrewise terminal objects if and only if each Fibre Category $\mathcal{E}_{X}$ has a Terminal Object $\top_{X}$, and every Base Change Functor $u^{*}:\mathcal{E}_{Y}\to\mathcal{E}_{X}$ preserves terminal objects.

  This is essentially an inlined version of