Definition fully_faithful_1cell_inv_map {B : bicat} {a b : B} {f : a --> b} (Hf : fully_faithful_1cell f) {z : B} {g₁ g₂ : z --> a} (αf : g₁ · f ==> g₂ · f) : g₁ ==> g₂ := pr1 (pr2 Hf _ _ _ αf).
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.