Definition mor_of_street_fib {B₁ B₂ E₁ E₂ : category} (P₁ : E₁ ⟶ B₁) (P₂ : E₂ ⟶ B₂) : UU := ∑ (FB : B₁ ⟶ B₂) (FE : E₁ ⟶ E₂), preserves_cartesian P₁ P₂ FE × nat_z_iso (P₁ ∙ FB) (FE ∙ P₂).
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.