Lemma compose_bifunctor_with_functor_data {A B C D : category} (F : bifunctor A B C) (G : functor C D) : bifunctor_data A B D. Proof. use make_bifunctor_data. - intros a b. exact (G (a ⊗_{F} b)). - intros a b1 b2 g. exact (#G (a ⊗^{F}_{l} g)). - intros a b1 b2 f. exact (#G (f ⊗^{F}_{r} a)). Defined.
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.