Definition id_mor_of_street_fib_nat_trans {B E : category} (P : E ⟶ B) : P ∙ functor_identity B ⟹ functor_identity E ∙ P. Proof. use make_nat_trans. - exact (λ _, identity _). - abstract (intros ? ? ? ; cbn ; rewrite id_left, id_right ; apply idpath). 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.