proposition: Lemma is_functor_BinCoproduct_of_functors_data : is_functor BinCoproduct_of_functors_data.
proof: Proof. split; simpl; intros. - unfold functor_idax; intros; simpl in *. apply pathsinv0. apply BinCoproduct_endo_is_identity. + unfold BinCoproduct_of_functors_mor. rewrite BinCoproductOfArrowsIn1. rewrite functor_id. apply id_left. + unfold BinCoproduct_of_functors_mor. rewrite BinCoproductOfArrowsIn2. rewrite functor_id. apply id_left. - unfold functor_compax, BinCoproduct_of_functors_mor; intros; simpl in *. unfold BinCoproduct_of_functors_mor. do 2 rewrite functor_comp. rewrite <- BinCoproductOfArrows_comp. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory