Lemma Strong_Functor_category_Pisset (F : [A, A']) : isaset (actionbased_strength Mon_V actn actn' F). 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.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrength.