Definition comp_mor_of_street_fib {B₁ B₂ B₃ E₁ E₂ E₃ : category} {P₁ : E₁ ⟶ B₁} {P₂ : E₂ ⟶ B₂} {P₃ : E₃ ⟶ B₃} (F₁ : mor_of_street_fib P₁ P₂) (F₂ : mor_of_street_fib P₂ P₃) : mor_of_street_fib P₁ P₃ := mor_of_street_fib_base F₁ ∙ mor_of_street_fib_base F₂ ,, mor_of_street_fib_total F₁ ∙ mor_of_street_fib_total F₂ ,, composition_preserves_cartesian (mor_of_street_fib_preserves_cartesian F₁) (mor_of_street_fib_preserves_cartesian F₂) ,, comp_mor_of_street_fib_nat_z_iso F₁ F₂.
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.