Definition is_binat_trans {F G : bifunctor_data A B C} (α : binat_trans_data F G) := (∏ (a : A) (b1 b2 : B) (g : B⟦b1,b2⟧), (a ⊗^{ F}_{l} g) · (α a b2) = (α a b1) · (a ⊗^{ G}_{l} g)) × (∏ (a1 a2 : A) (b : B) (f : A⟦a1,a2⟧), (f ⊗^{ F}_{r} b) · (α a2 b) = (α a1 b) · (f ⊗^{ G}_{r} b)).
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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.ProductCategory. Import BifunctorNotations. Import BifunctorNotations. Section FunctorsFromProductCategory. Import BifunctorNotations. End FunctorsFromProductCategory. Import BifunctorNotations. Import BifunctorNotations. Import BifunctorNotations.