proposition: Lemma Coproduct_endo_is_identity (a : I -> C) (CC : Coproduct a) (k : CoproductObject CC --> CoproductObject CC) (H1 : ∏ i, CoproductIn CC i · k = CoproductIn CC i) : identity _ = k.
proof: Proof. apply pathsinv0. eapply pathscomp0; [apply CoproductArrowEta|]. apply pathsinv0, CoproductArrowUnique; intro i; apply pathsinv0. now rewrite id_right, H1. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.whiskering