Definition mnd_bicat_of_cats_to_Monad (m : mnd bicat_of_cats) : Monad (ob_of_mnd m). Proof. simple refine (_,,((_ ,, _) ,, _)). - exact (endo_of_mnd m). - exact (mult_of_mnd m). - exact (unit_of_mnd m). - repeat split. + abstract (intro x ; cbn ; pose (nat_trans_eq_pointwise (mnd_unit_right m) x) as p ; cbn in p ; rewrite id_left in p ; exact p). + abstract (intro x ; cbn ; pose (nat_trans_eq_pointwise (mnd_unit_left m) x) as p ; cbn in p ; rewrite id_left in p ; exact p). + abstract (intro x ; cbn ; pose (nat_trans_eq_pointwise (mnd_mult_assoc m) x) as p ; cbn in p ; rewrite id_left in p ; exact (!p)). 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.