Definition pseudomonic_weq_fully_faithful_locally_grpd {B : bicat} (inv_B : locally_groupoid B) {a b : B} (f : a --> b) : pseudomonic_1cell f ≃ fully_faithful_1cell f. Proof. use weqimplimpl. - exact (pseudomonic_is_fully_faithful_locally_grpd inv_B). - exact fully_faithful_is_pseudomonic. - apply isaprop_pseudomonic_1cell. - apply isaprop_fully_faithful_1cell. 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.