Definition disp_bicat_of_strong_unit_type : disp_bicat bicat_full_comp_cat. Proof. use disp_subbicat. - exact (λ (C : full_comp_cat), ∑ (T : fiberwise_terminal (cleaving_of_types C)), ∏ (Γ : C), is_z_isomorphism (π (pr1 (pr1 T Γ)))). - exact (λ (C₁ C₂ : full_comp_cat) T₁ T₂ (F : full_comp_cat_functor C₁ C₂), ∏ (x : C₁), preserves_terminal (fiber_functor (comp_cat_type_functor F) x)). - abstract (intros C T x y Hy ; exact Hy). - abstract (intros C₁ C₂ C₃ T₁ T₂ T₃ F G HF HG x y Hy ; apply HG ; apply HF ; exact Hy). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Fiberwise.FiberwiseTerminal. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. 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.Sub1Cell. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.ComprehensionCat.BicatOfCompCat. Require Import UniMath.Bicategories.ComprehensionCat.CompCatNotations.