proposition: Lemma bifunctor_from_to {C D E : category} (F : functor C [D,E]) : bifunctor_to_functorintoendofunctorcat (bifunctor_from_functorintoendofunctorcat F) = F.
proof: Proof. use functor_eq. { apply homset_property. } use total2_paths_f. { cbn. apply idpath. } cbn. repeat (apply funextsec ; intro). use total2_paths_f. { apply idpath. } repeat (apply funextsec ; intro). apply E. 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