Definition fully_faithful_op2_bicat {B : bicat} {x y : B} {f : x --> y} (Hf : fully_faithful_1cell f) : @fully_faithful_1cell (op2_bicat B) _ _ f. Proof. use make_fully_faithful. - apply faithful_op2_bicat. apply fully_faithful_1cell_faithful. exact Hf. - intros z g₁ g₂ αf. simple refine (_ ,, _). + exact (fully_faithful_1cell_inv_map Hf αf). + cbn. apply fully_faithful_1cell_inv_map_eq. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.FullyFaithful. Require Import UniMath.Bicategories.Morphisms.DiscreteMorphisms.