proposition: Lemma Strong_Functor_category_Pisset (F : [A, A']) : isaset (actionbased_strength Mon_V actn actn' F).
proof: Proof. change isaset with (isofhlevel 2). apply isofhleveltotal2. - use (functor_category_has_homsets (A ⊠ Mon_V)). apply homset_property. - intro ϛ. apply isasetaprop. apply isapropdirprod. + apply isaprop_actionbased_strength_triangle_eq. + apply isaprop_actionbased_strength_pentagon_eq. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ActionBasedStrength