Definition map2cells_disp_cat_data : disp_cat_ob_mor (map1cells C D). Proof. use tpair. - exact (λ F, ∏ (X Y : C) (f g : X --> Y), f ==> g → Fmor F f ==> Fmor F g). - exact (λ F G F₂ G₂ η, ∏ (X Y : C) (f g : X --> Y) (α : f ==> g), (ηobj η X ◃ G₂ X Y f g α) • ηmor η g = ηmor η f • (F₂ X Y f g α ▹ ηobj η Y)) ; cbn in *. 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.PseudoFunctors.Display.Map1Cells. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.