Definition twosided_disp_functor_comp_law (FG : twosided_disp_functor_data) : UU := ∏ (x₁ x₂ x₃ : C₁) (y₁ y₂ y₃ : C₂) (xy₁ : D₁ x₁ y₁) (xy₂ : D₁ x₂ y₂) (xy₃ : D₁ x₃ y₃) (f₁ : x₁ --> x₂) (g₁ : y₁ --> y₂) (fg₁ : xy₁ -->[ f₁ ][ g₁ ] xy₂) (f₂ : x₂ --> x₃) (g₂ : y₂ --> y₃) (fg₂ : xy₂ -->[ f₂ ][ g₂ ] xy₃), #2 FG (fg₁ ;;2 fg₂) = transportb_disp_mor2 (functor_comp F f₁ f₂) (functor_comp G g₁ g₂) (#2 FG fg₁ ;;2 #2 FG fg₂).
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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Section FromDispFunctor. End FromDispFunctor.