proposition: Lemma colimOfArrowsIn {C : precategory} {g : graph} (d1 d2 : diagram g C) (CC1 : ColimCocone d1) (CC2 : ColimCocone d2) (f : ∏ (u : vertex g), C⟦dob d1 u,dob d2 u⟧) (fNat : ∏ u v (e : edge u v), dmor d1 e · f v = f u · dmor d2 e) : ∏ u, colimIn CC1 u · colimOfArrows CC1 CC2 f fNat = f u · colimIn CC2 u.
proof: Proof. now unfold colimOfArrows; intro u; rewrite colimArrowCommutes. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Propositions 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.Adjunctions.Core