Definition conservative_1cell {B : bicat} {a b : B} (f : a --> b) : UU := ∏ (x : B) (g₁ g₂ : x --> a) (α : g₁ ==> g₂), is_invertible_2cell (α ▹ f) → is_invertible_2cell α.
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. Require Import UniMath.Bicategories.Morphisms.FullyFaithful.