proposition: Lemma bifunctor_to_functorintoendofunctorcat_data_is_functor {C D E : category} (F : bifunctor C D E) : is_functor (bifunctor_to_functorintoendofunctorcat_data F).
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.ProductCategory