proposition: Lemma ad_is_algebra_mor : is_algebra_mor _ α_alg Aa ad.
proof: Proof. apply pathsinv0, z_iso_inv_to_left, colimArrowUnique; simpl; intro n. destruct n as [|n]. - now apply InitialArrowUnique. - rewrite assoc, unfold_inv_from_z_iso_α. eapply pathscomp0; [apply cancel_postcomposition, (colimArrowCommutes shiftColimCocone)|]. simpl; rewrite assoc, <- functor_comp. apply cancel_postcomposition, maponpaths, (colimArrowCommutes CC). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.Chains.Chains