Lemma bifunctor_to_functorintoendofunctorcat_data_is_functor {C D E : category} (F : bifunctor C D E) : is_functor (bifunctor_to_functorintoendofunctorcat_data F). Proof. use tpair. + intro c. use nat_trans_eq. { apply homset_property. } intro ; apply bifunctor_rightid. + intros c1 c2 c3 f g. use nat_trans_eq. { apply homset_property. } intro ; apply bifunctor_rightcomp. Qed.
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.