Definition bifunctor_data_from_functorintoendofunctorcat_is_bifunctor {C D E : category} (F : functor C [D,E]) : is_bifunctor (bifunctor_data_from_functorintoendofunctorcat F). Proof. repeat (use tpair). + intro ; intro ; apply functor_id. + abstract (exact (λ d c, eqtohomot (maponpaths pr1 (functor_id F c)) d)). + intro ; intros ; apply functor_comp. + abstract (intro ; intros; exact (eqtohomot (maponpaths pr1 (functor_comp F f1 f2)) b)). + abstract (intro ; intros; exact (! pr2 (#F f) b1 b2 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.