Definition bifunctor_to_functorintoendofunctorcat_data {C D E : category} (F : bifunctor C D E) : functor_data C [D,E]. Proof. use make_functor_data. - exact (λ c, leftwhiskering_functor F c). - intros c1 c2 f. exists (λ d, f ⊗^{F}_{r} d). abstract (exact (λ d1 d2 g, ! bifunctor_equalwhiskers F c1 c2 d1 d2 f g)). 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.