Definition faithful_1cell {B : bicat} {a b : B} (f : a --> b) : UU := ∏ (z : B) (g₁ g₂ : z --> a) (α₁ α₂ : g₁ ==> g₂), α₁ ▹ f = α₂ ▹ f → α₁ = α₂.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells.