Definition psfunctor_on_mnd_cell {B₁ B₂ : bicat} (F : psfunctor B₁ B₂) {m₁ m₂ : mnd B₁} {f g : m₁ --> m₂} (τ : f ==> g) : psfunctor_on_mnd_mor F f ==> psfunctor_on_mnd_mor F g. Proof. use make_mnd_cell. - exact (##F (cell_of_mnd_cell τ)). - abstract (unfold is_mnd_cell ; cbn -[psfunctor_comp psfunctor_id] ; rewrite !vassocr ; rewrite <- psfunctor_rwhisker ; rewrite !vassocl ; apply maponpaths ; rewrite !vassocr ; rewrite <- psfunctor_vcomp ; rewrite <- (mnd_cell_endo τ) ; rewrite !psfunctor_vcomp ; rewrite !vassocl ; apply maponpaths ; use vcomp_move_R_pM ; [ is_iso | ] ; rewrite !vassocr ; use vcomp_move_L_Mp ; [ is_iso | ] ; cbn -[psfunctor_comp psfunctor_id] ; rewrite psfunctor_lwhisker ; 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.