proposition: Lemma Signature_category_Pisset (H : [[C, D'], [C, D]]) : isaset (@StrengthForSignature C D D' H).
proof: Proof. change isaset with (isofhlevel 2). apply isofhleveltotal2. { apply (functor_category_has_homsets ([C, D'] ⊠ category_Ptd C) ([C, D]) (functor_category_has_homsets _ _ _)). } intro θ. apply isasetaprop. apply isapropdirprod. + apply isaprop_θ_Strength1_int. + apply isaprop_θ_Strength2_int. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.FunctorCategory UniMath.SubstitutionSystems.Notation UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Core.Univalence UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SumOfSignatures