Definition composition_preserves_cartesian {B₁ B₂ B₃ E₁ E₂ E₃ : category} {P₁ : E₁ ⟶ B₁} {P₂ : E₂ ⟶ B₂} {P₃ : E₃ ⟶ B₃} {FE₁ : E₁ ⟶ E₂} {FE₂ : E₂ ⟶ E₃} (HFE₁ : preserves_cartesian P₁ P₂ FE₁) (HFE₂ : preserves_cartesian P₂ P₃ FE₂) : preserves_cartesian P₁ P₃ (FE₁ ∙ FE₂).
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.