Lemma bifunctor_equiv_functorintoendofunctorcat (C D E : category) : bifunctor C D E ≃ functor C [D,E]. Proof. use weq_iso. { apply bifunctor_to_functorintoendofunctorcat. } { apply bifunctor_from_functorintoendofunctorcat. } { intro ; apply bifunctor_to_from. } { intro ; apply bifunctor_from_to. } Defined.
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.