Proposition make_is_left_extension {h : y --> z} (τ : f ==> g · h) (F : ∏ (k : y --> z) (θ : f ==> g · k), h ==> k) (HF₁ : ∏ (k : y --> z) (θ : h ==> k), F k (τ • (g ◃ θ)) = θ) (HF₂ : ∏ (k : y --> z) (θ : f ==> g · k), τ • (g ◃ F k θ) = θ) : is_left_extension τ. Proof. intros k. use isweq_iso. - exact (F k). - exact (HF₁ k). - exact (HF₂ k). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat.