Definition double_functor_runitor {C₁ C₂ : category} {F : C₁ ⟶ C₂} {D₁ : twosided_disp_cat C₁ C₁} {D₂ : twosided_disp_cat C₂ C₂} {I₁ : hor_id D₁} {Cm₁ : hor_comp D₁} {I₂ : hor_id D₂} {Cm₂ : hor_comp D₂} (r₁ : double_cat_runitor I₁ Cm₁) (r₂ : double_cat_runitor I₂ Cm₂) {FF : twosided_disp_functor F F D₁ D₂} (FI : double_functor_hor_id FF I₁ I₂) (FC : double_functor_hor_comp FF Cm₁ Cm₂) : UU := ∏ (x y : C₁) (f : D₁ x y), double_runitor r₂ (FF _ _ f) = transportf_disp_mor2 (assoc' _ _ _ @ id_left _ @ id_left _ @ functor_id F _) (assoc' _ _ _ @ id_left _ @ id_left _ @ functor_id F _) (double_hor_comp_mor Cm₂ (id_two_disp _) (functor_double_id_cell FI _) ;;2 functor_double_comp_cell FC _ _ ;;2 #2 FF (double_runitor r₁ f)).
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.