Definition path_twosided_disp_functor_mor {C₁ C₂ C₁' C₂' : category} {F : C₁ ⟶ C₁'} {G : C₂ ⟶ C₂'} {D : twosided_disp_cat C₁ C₂} {D' : twosided_disp_cat C₁' C₂'} {FG FG' : twosided_disp_functor F G D D'} (p : FG = FG') {x₁ x₂ : C₁} {f : x₁ --> x₂} {y₁ y₂ : C₂} {g : y₁ --> y₂} {xy₁ : D x₁ y₁} {xy₂ : D x₂ y₂} (fg : xy₁ -->[ f ][ g ] xy₂) : #2 FG fg = transportf_disp_mor2 (id_right _ @ id_left _) (id_right _ @ id_left _) (idtoiso_twosided_disp (idpath _) (idpath _) (path_twosided_disp_functor_ob p xy₁) ;;2 #2 FG' fg ;;2 idtoiso_twosided_disp (idpath _) (idpath _) (!(path_twosided_disp_functor_ob p xy₂))).
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Categories.CategoryOfSetCategories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.DispFunctorPair. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedNatTrans. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TransportLaws. Section FromIso. End FromIso.