Lemma monoid_to_disp_Monad_laws : disp_Monad_laws monoid_to_disp_Monad_data. Proof. repeat split. - intro c. set (t := monoid_right_unit_law _ M). exact (eqtohomot (base_paths _ _ t) c). - intro c. set (t := monoid_left_unit_law _ M). exact (eqtohomot (base_paths _ _ t) c). - intro c. set (t := monoid_assoc_law _ M). refine (! (eqtohomot (base_paths _ _ t) c) @ _). etrans. 1: apply assoc'. apply id_left. 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.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.