Definition double_functor_hor_comp_data {C₁ C₂ : category} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {F : C₁ ⟶ C₂} (FF : twosided_disp_functor F F D₁ D₂) (Cm₁ : hor_comp D₁) (Cm₂ : hor_comp D₂) : UU := ∏ (x y z : C₁) (h : D₁ x y) (k : D₁ y z), double_hor_comp Cm₂ (FF _ _ h) (FF _ _ k) -->[ identity _ ][ identity _ ] FF _ _ (double_hor_comp Cm₁ h k).
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.