Definition psfunctor_on_mnd_id_mor {B₁ B₂ : bicat} (F : psfunctor B₁ B₂) (m : mnd B₁) : id₁ _ ==> psfunctor_on_mnd_mor F (id₁ m). Proof. use make_mnd_cell. - unfold mnd_cell_data. exact (psfunctor_id F _). - abstract (unfold is_mnd_cell ; cbn -[psfunctor_id psfunctor_comp] ; rewrite !vassocl ; rewrite !psfunctor_vcomp ; rewrite psfunctor_lunitor ; rewrite !vassocl ; do 3 apply maponpaths ; rewrite psfunctor_rinvunitor ; rewrite !vassocl ; rewrite vcomp_rinv ; rewrite id2_right ; 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.DisplayedCats.Core. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EndoMap. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations.