Definition make_comp_cat_dependent_sum {C : comp_cat} (sig : ∏ (Γ : C) (A : ty Γ), dependent_sum (cleaving_of_types C) (π A)) (stable : ∏ (Γ₁ Γ₂ : C) (A₁ : ty Γ₁) (A₂ : ty Γ₂) (s₁ : Γ₁ --> Γ₂) (s₂ : Γ₁ & A₁ --> Γ₂ & A₂) (p : s₂ · π A₂ = π A₁ · s₁) (Hp : isPullback p), left_beck_chevalley _ (π A₂) s₁ (π A₁) s₂ p (sig _ A₂) (sig _ A₁)) : comp_cat_dependent_sum C := sig ,, stable.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.DependentSums. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInBicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Examples.MorphismsInOp1Bicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.LiftDispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations.