fact: Definition GenMendlerIteration : ∏ (C : category) (F : functor C C) (μF_Initial : Initial (FunctorAlg F)) (C' : category) (X : C') (L : functor C C'), is_left_adjoint L → ∏ ψ : ψ_source C C' X L ⟹ ψ_target C F C' X L, ∃! h : C' ⟦ L ` (InitialObject μF_Initial), X ⟧, # L (alg_map F (InitialObject μF_Initial)) · h = ψ ` (InitialObject μF_Initial) h.
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