Definition orthogonal_factorization_system (B : bicat) : UU := ∑ (L R : ∏ (x y : B), x --> y → hProp), (∏ (x y : B) (f : x --> y), factorization_1cell L R f) × closed_under_invertible_2cell L × closed_under_invertible_2cell R × orthogonal_maps L R.
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.