proposition: Lemma weqSignatureLaxMorphismActegories_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: Proof. apply (weqcomp weqSignatureLaxMorphismActegories). apply weqfibtototal. intro H. exact (idweq _). Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored UniMath.Bicategories.MonoidalCategories.PointedFunctorsMonoidal UniMath.Bicategories.MonoidalCategories.Actions UniMath.Bicategories.MonoidalCategories.ConstructionOfActions UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicat UniMath.Bicategories.MonoidalCategories.ActionBasedStrength UniMath.Bicategories.MonoidalCategories.MonoidalFromBicategory UniMath.Bicategories.MonoidalCategories.ActionBasedStrongFunctorCategory UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfCats UniMath.CategoryTheory.Monoidal.Examples.EndofunctorsMonoidalElementary UniMath.CategoryTheory.Actegories.Examples.ActionOfEndomorphismsInCATElementary UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.ActionBasedStrengthOnHomsInBicat UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects UniMath.Bicategories.MonoidalCategories.PointedFunctorsWhiskeredMonoidal UniMath.Bicategories.MonoidalCategories.ActionOfEndomorphismsInBicatWhiskered UniMath.Bicategories.MonoidalCategories.BicatOfActegories