Definition locally_groupoid_if_pseudomonic {C : category} (D : disp_cat C) (H : pseudomonic_disp_cat D) : groupoidal_disp_cat D. Proof. intros x y f Hf xx yy ff. simple refine (_ ,, (_ ,, _)). + exact (pr2 H y x (z_iso_inv (f ,, Hf)) yy xx). + apply H. + apply H. 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.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.