proposition: Lemma composition_functor_with_bifunctor_isbifunctor {A B A' B' C : category} (F : functor A A') (G : functor B B') (H : bifunctor A' B' C) : is_bifunctor (compose_functor_with_bifunctor_data F G H).
proof: Proof. repeat split. - intros a b. cbn. rewrite functor_id. apply bifunctor_leftid. - intros a b. cbn. rewrite functor_id. apply bifunctor_rightid. - intros a b1 b2 b3 g1 g2. cbn. rewrite functor_comp. apply bifunctor_leftcomp. - intros b a1 a2 a3 f1 f2. cbn. rewrite functor_comp. apply bifunctor_rightcomp. - intros a1 a2 b1 b2 f g. apply (whiskerscommutes H (bifunctor_equalwhiskers H)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.ProductCategory