Definition comp_hor_comp {C₁ C₂ C₃ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {D₃ : twosided_disp_cat C₃ C₃} {Cm₁ : hor_comp D₁} {Cm₂ : hor_comp D₂} {Cm₃ : hor_comp D₃} {F : C₁ ⟶ C₂} {FF : twosided_disp_functor F F D₁ D₂} {G : C₂ ⟶ C₃} {GG : twosided_disp_functor G G D₂ D₃} (HFF : double_functor_hor_comp FF Cm₁ Cm₂) (HGG : double_functor_hor_comp GG Cm₂ Cm₃) : double_functor_hor_comp (comp_twosided_disp_functor FF GG) Cm₁ Cm₃. Proof. use make_double_functor_hor_comp. - exact (comp_hor_comp_data HFF HGG). - exact (comp_hor_comp_laws HFF HGG). 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.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics.