Lemma bifunctor_from_to {C D E : category} (F : functor C [D,E]) : bifunctor_to_functorintoendofunctorcat (bifunctor_from_functorintoendofunctorcat F) = F. 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.
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.