Lemma leftwhiskering_functor_pre (F : bifunctor_data) (bli : bifunctor_leftidax F) (blc : bifunctor_leftcompax F) (a : A): functor B C. Proof. use make_functor. - use tpair. + intro b. exact (a ⊗_{F} b). + intros b1 b2 g. exact (a ⊗^{F}_{l} g). - use tpair. + intros b. exact (bli a b). + intros b1 b2 b3 g2 g3. cbn. exact (blc a b1 b2 b3 g2 g3). 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.