Lemma weqSignatureLaxMorphismActegories_alt_alt : Signature C D D' ≃ hom(C:=actbicat Mon_ptdendo) (hom(C:=bicat_of_cats) C D',,actegoryPtdEndosOnFunctors D') (hom(C:=bicat_of_cats) C D,,actegoryPtdEndosOnFunctors D). Proof. apply (weqcomp weqSignatureABStrength). apply weqfibtototal. intro H. apply weqABStrengthLaxMorphismActegories. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.Bicategories.MonoidalCategories.PointedFunctorsMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.Actions. Require Import UniMath.Bicategories.MonoidalCategories.ConstructionOfActions. Require Import UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicat. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrength. Require Import UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory. Require Import UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorCategory. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary. Require Import UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary. Require Import UniMath.SubstitutionSystems.Signatures. Require Import UniMath.SubstitutionSystems.ActionBasedStrengthOnHomsInBicat. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Require Import UniMath.Bicategories.MonoidalCategories.PointedFunctorsWhiskeredMonoidal. Require Import UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicatWhiskered. Require Import UniMath.Bicategories.MonoidalCategories.BicatOfActegories. Import Bicat.Notations. Import MonoidalNotations.