Definition op1_mnd_cell_weq_mnd_opcell {B : bicat} {m₁ m₂ : op1_bicat (mnd (op1_bicat B))} (f₁ f₂ : m₁ --> m₂) : f₁ ==> f₂ ≃ mnd_opcell (op1_mnd_mor_to_mnd_opmor f₁) (op1_mnd_mor_to_mnd_opmor f₂). Proof. use make_weq. - exact op1_mnd_cell_to_mnd_opcell. - use isweq_iso. + exact mnd_opcell_to_op1_mnd_cell. + abstract (intro α ; use eq_mnd_cell ; apply idpath). + abstract (intro α ; use subtypePath ; [ intro ; apply cellset_property | ] ; apply idpath). 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.DisplayedCats.Core. 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.Examples.OpMorBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Import DispBicat.Notations. Require Import UniMath.Bicategories.DisplayedBicats.Examples.MonadsLax.