Definition closed_under_invertible_2cell {B : bicat} (P : ∏ (x y : B), x --> y → hProp) : UU := ∏ (x y : B) (f g : x --> y) (τ : invertible_2cell f g), P _ _ f → P _ _ g.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.OrthogonalFactorization.Orthogonality.