Definition strict_compositor_disp_cat_data : disp_cat_ob_mor (map1cells C D). Proof. use tpair. - exact (λ F, ∏ (X Y Z : C) (f : X --> Y) (g : Y --> Z), Fmor F f · Fmor F g = Fmor F (f · g)). - exact (λ F G Fcomp Gcomp η, ∏ (X Y Z : C) (f : X --> Y) (g : Y --> Z), (ηobj η X ◃ idtoiso_2_1 _ _ (Gcomp X Y Z f g)) • ηmor η (f · g) = (lassociator (ηobj η X) (Fmor G f) (Fmor G g)) • (ηmor η f ▹ (Fmor G g)) • rassociator (Fmor F f) (ηobj η Y) (Fmor G g) • (Fmor F f ◃ ηmor η g) • lassociator (Fmor F f) (Fmor F g) (ηobj η Z) • (idtoiso_2_1 _ _ (Fcomp X Y Z f g) ▹ ηobj η Z)). 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.