proposition: Lemma SigmaMonoid_is_compatible (σ : SigmaMonoid) : SigmaMonoid_characteristic_equation (SigmaMonoid_carrier σ) (SigmaMonoid_η σ) (SigmaMonoid_μ σ) (SigmaMonoid_τ σ) (pr1 θ (SigmaMonoid_carrier σ ,, SigmaMonoid_η σ) (SigmaMonoid_carrier σ)).
proof: Proof. exact (pr22 σ). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Examples.Sigma UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Actegories.MorphismsOfActegories UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.FunctorAlgebras UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems