proposition: Lemma CoproductOfArrowsInclusionIn {I J : UU} {C : category} (incl : I -> J) {a : I -> C} (CCab : Coproduct _ _ a) {c : J -> C} (CCcd : Coproduct _ _ c) (f : ∏ i, a i --> c (incl i)) : ∏ i, CoproductIn _ _ CCab i · CoproductOfArrowsInclusion incl CCab CCcd f = f i · CoproductIn _ _ CCcd (incl i).
proof: Proof. unfold CoproductOfArrows; intro i. apply CoproductInCommutes. 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