Definition monoid_equiv_monoid : MON ≃ Monad C. Proof. use weq_iso. - apply monoid_to_monad. - apply monad_to_monoid. - abstract (intro M; use total2_paths_f; [apply idpath | use total2_paths_f; [apply idpath | apply isaprop_monoid_laws]]). - abstract (intro M; use total2_paths_f; [apply idpath | use total2_paths_f; [apply idpath | apply isaprop_disp_Monad_laws]]). Defined.
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.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Import BifunctorNotations. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids. Require Import UniMath.Bicategories.MonoidalCategories.EndofunctorsWhiskeredMonoidal. Require Import UniMath.CategoryTheory.Monads.Monads.