Definition make_factorization_1cell {B : bicat} {L R : ∏ (x y : B), x --> y → hProp} {x y : B} {f : x --> y} (a : B) (l : x --> a) (r : a --> y) (Ll : L _ _ l) (Rr : R _ _ r) (τ : invertible_2cell (l · r) f) : factorization_1cell L R f := a ,, l ,, r ,, Ll ,, Rr ,, τ.
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.