Definition comp_cat_dependent_sum (C : comp_cat) : UU := ∑ (sig : ∏ (Γ : C) (A : ty Γ), dependent_sum (cleaving_of_types C) (π A)), ∏ (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).
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.