Definition mnd_bicat_of_cats_weq_Monad : mnd bicat_of_cats ≃ ∑ (C : category), Monad C. Proof. use make_weq. - exact (λ m, ob_of_mnd m ,, mnd_bicat_of_cats_to_Monad m). - use isweq_iso. + exact (λ m, Monad_to_mnd_bicat_of_cats (pr2 m)). + exact mnd_bicat_of_cats_weq_Monad_inv₁. + abstract (intro m ; refine (maponpaths (λ z, pr1 m ,, z) _) ; exact (mnd_bicat_of_cats_weq_Monad_inv₂ (pr2 m))). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Monads.Monads. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax.