Definition is_disp_binat_trans {A B C : category} {F : bifunctor_data A B C} {G : bifunctor_data A B C} {DA : disp_cat A} {DB : disp_cat B} {DC : disp_cat C} {α : binat_trans F G} {DF : disp_bifunctor_data F DA DB DC} {DG : disp_bifunctor_data G DA DB DC} (dα : disp_binat_trans_data α DF DG) : UU := (∏ (x : A) (y1 y2 : B) (g : B⟦y1,y2⟧) (xx : DA x) (yy1 : DB y1) (yy2 : DB y2) (gg : yy1 -->[g] yy2), ((xx ⊗⊗^{DF}_{l} gg) ;; (dα _ _ xx yy2) = transportb _ (pr1 (pr2 α) x y1 y2 _) ((dα _ _ xx yy1) ;; (xx ⊗⊗^{DG}_{l} gg)))) × (∏ (x1 x2 : A) (y : B) (f : A⟦x1,x2⟧) (xx1 : DA x1) (xx2 : DA x2) (yy : DB y) (ff : xx1 -->[f] xx2), ((ff ⊗⊗^{DF}_{r} yy) ;; (dα _ _ xx2 yy) = transportb _ (pr2 (pr2 α) x1 x2 y _) ((dα _ _ xx1 yy) ;; (ff ⊗⊗^{DG}_{r} yy)))).
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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Core.Isos. Import BifunctorNotations. Import DisplayedBifunctorNotations.