Definition Monad_to_mnd_bicat_of_cats {C : category} (m : Monad C) : mnd bicat_of_cats. Proof. use make_mnd. - use make_mnd_data. + exact C. + cbn. exact m. + exact (η m). + exact (μ m). - repeat split. + abstract (use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; rewrite id_left ; apply (Monad_law2(T:=m) x)). + abstract (use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; rewrite id_left ; apply (Monad_law1(T:=m) x)). + abstract (use nat_trans_eq ; [ apply homset_property | ] ; intro x ; cbn ; rewrite id_left ; refine (!_) ; apply (Monad_law3(T:=m) x)). 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.