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. exact (pr22 σ). Qed.
Require Import UniMath.Foundations.All. 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.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Sigma. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.CategoryTheory.FunctorAlgebras. Require Import UniMath.SubstitutionSystems.GeneralizedSubstitutionSystems. Import BifunctorNotations.