proposition: Lemma is_functor_bincoproduct_functor_data {C : category} (PC : BinCoproducts C) : is_functor (bincoproduct_functor_data PC).
proof: Proof. split. - intro x; simpl; apply pathsinv0. use BinCoproduct_endo_is_identity. + now rewrite BinCoproductOfArrowsIn1, id_left. + now rewrite BinCoproductOfArrowsIn2, id_left. - now intros x y z f g; simpl; rewrite BinCoproductOfArrows_comp. 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