proposition: Lemma bifunctor_equiv_functorfromproductcat (C D E : category) : bifunctor C D E ≃ functor (category_binproduct C D) E.
proof: Proof. use weq_iso. { apply bifunctor_to_functorfromproductcat. } { apply bifunctor_from_functorfromproductcat. } { intro ; apply bifunctor_to_functor_to_bifunctor. } intro ; apply functor_to_bifunctor_to_functor. Defined.
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