Definition id_mor_of_street_fib_nat_z_iso {B E : category} (P : E ⟶ B) : nat_z_iso (P ∙ functor_identity B) (functor_identity E ∙ P). Proof. use make_nat_z_iso. - exact (id_mor_of_street_fib_nat_trans P). - intro x. cbn. apply identity_is_z_iso. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations.