Definition is_mnd (m : mnd_data) : UU := let X := pr1 m in let f := pr12 m in let η := pr122 m in let μ := pr222 m in (linvunitor f • (η ▹ f) • μ = id2 f) × (rinvunitor f • (f ◃ η) • μ = id2 f) × (rassociator _ _ _ • (f ◃ μ) • μ = (μ ▹ f) • μ).
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.Univalence. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Projection. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence. Require Import UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.DisplayedBicats.Examples.FullSub. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap.