Definition double_nat_trans_hor_comp {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {F G : C₁ ⟶ C₂} {FF : twosided_disp_functor F F D₁ D₂} {GG : twosided_disp_functor G G D₁ D₂} {τ : F ⟹ G} (ττ : twosided_disp_nat_trans τ τ FF GG) {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} (FC : double_functor_hor_comp FF Cm₁ Cm₂) (GC : double_functor_hor_comp GG Cm₁ Cm₂) : UU := ∏ (x y z : C₁) (h : D₁ x y) (k : D₁ y z), functor_double_comp_cell FC h k ;;2 ττ _ _ (double_hor_comp Cm₁ h k) = transportb_disp_mor2 (id_left _ @ !(id_right _)) (id_left _ @ !(id_right _)) (double_hor_comp_mor Cm₂ (ττ _ _ h) (ττ _ _ k) ;;2 functor_double_comp_cell GC h k).
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.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleFunctor.