proposition: Lemma bracket_Thm15_ok_η : ∏ (C : category) (CP : BinCoproducts C) (KanExt : ∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C) (H : Presignature C C C) (IA : Initial (FunctorAlg (Id_H C CP H))) (Z : category_Ptd C) (f : [C,C] ⟦ U Z, U (ptd_from_alg (InitAlg C CP H IA))⟧), f = # (pr1 (ℓ (U Z))) (η (InitAlg C CP H IA)) · bracket_Thm15 C CP KanExt H IA Z f.
proof: Proof. apply bracket_Thm15_ok_part1. Qed.
imports: UniMath.Foundations.PartD UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Monads UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.BinSumOfSignatures UniMath.SubstitutionSystems.SimplifiedHSS.SubstitutionSystems UniMath.SubstitutionSystems.GenMendlerIteration UniMath.CategoryTheory.RightKanExtension UniMath.SubstitutionSystems.GenMendlerIteration UniMath.SubstitutionSystems.SimplifiedHSS.LiftingInitial UniMath.SubstitutionSystems.SimplifiedHSS.MonadsFromSubstitutionSystems UniMath.SubstitutionSystems.LamSignature UniMath.SubstitutionSystems.SimplifiedHSS.Lam UniMath.SubstitutionSystems.Notation