Identity Displayed Category

The identity displayed category $\mathrm{Id}:\mathcal{B}\rightarrowtriangle\mathcal{B}$ is the Displayed Category that has a single object displayed over each object $X:\mathcal{B}$, and a single displayed morphism over each morphism in $\mathcal{B}$. This corresponds to the identity Functor when viewed through the fibred point of view.

Properties

• The identity displayed category is both a Cocartesian Fibration and Cartesian Fibration; in fact it is both a Right Fibration and a Left Fibration.