Definition trivial_lift_1cell {x₃ : B₁} {y₃ : trivial_displayed_bicat B₁ B₂ x₃} (h : x₃ --> x₁) (k : y₃ -->[ h · f] y₂) : lift_1cell_factor (trivial_displayed_bicat B₁ B₂) g k. Proof. simple refine (_ ,, _) ; cbn in *. - exact (k · left_adjoint_right_adjoint Hg). - simple refine (_ ,, _) ; cbn. + refine (rassociator _ _ _ • (k ◃ _) • runitor _). exact (left_adjoint_counit Hg). + cbn. use trivial_is_invertible_2cell_to_is_disp_invertible. is_iso. apply (left_equivalence_counit_iso Hg). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.Properties. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Fibrations. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.CleavingOfBicat. Require Import UniMath.Bicategories.DisplayedBicats.Cartesians. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Trivial.