6.1.2. Example: Revisiting the canonical self-indexing [002X]

Recall that the canonical self-indexing $\SelfIx{B}$ (Construction 2.1·a [001X]) of a category $B$ is a displayed category with $\SelfIx{B}\Sub{x} = \Sl{B}{x}$. As discussed in Exercise 2.1·b [001Y], $\SelfIx{B}$ is a cartesian fibration over $B$ if and only if $B$ has pullbacks. However, $\SelfIx{B}$ is unconditionally a cocartesian fibration.

[002Y] Exercise 6.1.2·a.

Prove that $\SelfIx{B}$ from [001X] is a cocartesian fibration for any category $B$.