Lemma compose_functor_with_bifunctor_data {A B A' B' C : category} (F : functor A A') (G : functor B B') (H : bifunctor A' B' C) : bifunctor_data A B C. Proof. use make_bifunctor_data. - intros a b. exact ((F a) ⊗_{H} (G b)). - intros a b1 b2 g. exact ((F a) ⊗^{H}_{l} (#G g)). - intros b a1 a2 f. exact ((#F f) ⊗^{H}_{r} (G b)). 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.