Definition map1cells_disp_cat_id_comp : disp_cat_id_comp (ps_base C D) map1cells_disp_cat. Proof. use tpair. - cbn. refine (λ F₀ F₁ X Y f, (lunitor (F₁ X Y f) • rinvunitor (F₁ X Y f) ,, _)). is_iso. - cbn. refine (λ F₀ G₀ H₀ η₁ ε₁ F₁ G₁ H₁ η₂ ε₂ X Y f, (rassociator (η₁ X) (ε₁ X) (H₁ X Y f)) • (η₁ X ◃ ε₂ X Y f) • lassociator (η₁ X) (G₁ X Y f) (ε₁ Y) • (η₂ X Y f ▹ ε₁ Y) • rassociator (F₁ X Y f) (η₁ Y) (ε₁ Y) ,, _). is_iso. + apply ε₂. + apply η₂. 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.PrecategoryBinProduct. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Display.Base. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.