Definition free_alg_1cell_cone : em_cone m. Proof. use make_em_cone. - exact x. - exact f. - exact (μ • linvunitor _). - abstract (refine (!(id2_left _) @ _) ; rewrite !vassocr ; apply maponpaths_2 ; refine (!_) ; exact (mnd_unit_right m)). - abstract (rewrite !vassocr ; apply maponpaths_2 ; rewrite !vassocl ; use vcomp_move_R_pM ; [ is_iso | ] ; cbn ; rewrite !vassocr ; rewrite rwhisker_vcomp ; rewrite !vassocl ; rewrite linvunitor_lunitor ; rewrite id2_right ; rewrite !vassocr ; exact (!(mnd_mult_assoc m))). Defined.
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.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Limits.EilenbergMooreObjects. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.Monads.Examples.AdjunctionToMonad. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.MonadInclusion.