Definition factorization_1cell {B : bicat} (L R : ∏ (x y : B), x --> y → hProp) {x y : B} (f : x --> y) : UU := ∑ (a : B) (l : x --> a) (r : a --> y), L _ _ l × R _ _ r × invertible_2cell (l · r) f.
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.