Definition mnd_to_cat_unit : functor_identity _ ⟹ mnd_to_functor. Proof. use make_nat_trans. - exact (λ f, rinvunitor _ • (f ◃ unit_of_mnd m)). - abstract (intros f g α ; cbn ; rewrite !vassocr ; rewrite rinvunitor_natural ; rewrite <- rwhisker_hcomp ; rewrite !vassocl ; rewrite vcomp_whisker ; apply idpath). 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.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monads.Monads. 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.DisplayedBicats.Examples.MonadsLax.