Definition pseudomonic_is_fully_faithful_locally_grpd {B : bicat} (inv_B : locally_groupoid B) {a b : B} {f : a --> b} (Hf : pseudomonic_1cell f) : fully_faithful_1cell f. Proof. use make_fully_faithful. - exact (pr1 Hf). - intros z g₁ g₂ αf. simple refine (_ ,, _). + use (pseudomonic_1cell_inv_map Hf αf). apply inv_B. + apply (pseudomonic_1cell_inv_map_eq Hf). Defined.
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.