proposition: Lemma precompWithCoproductArrowInclusion {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)) {x : C} (k : ∏ i, c i --> x) : CoproductOfArrowsInclusion incl CCab CCcd f · CoproductArrow _ _ CCcd k = CoproductArrow _ _ CCab (λ i, f i · k (incl i)).
proof: Proof. apply CoproductArrowUnique; intro i. now rewrite assoc, CoproductOfArrowsInclusionIn, <- assoc, 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