Lemma rightwhiskering_functor_pre (F : bifunctor_data) (bri : bifunctor_rightidax F) (brc : bifunctor_rightcompax F) (b : B) : functor A C. Proof. use make_functor. - use tpair. + intro a. exact (a ⊗_{F} b). + intros a1 a2 f. exact (f ⊗^{F}_{r} b). - use tpair. + intros a. exact (bri b a). + intros a1 a2 a3 f2 f3. cbn. exact (brc b a1 a2 a3 f2 f3). 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.