Definition grpds_iso_comma_pb_cone {C₁ C₂ C₃ : grpds} (F : C₁ --> C₃) (G : C₂ --> C₃) : pb_cone F G. Proof. use make_pb_cone. - exact (univalent_iso_comma (pr1 F) (pr1 G) ,, is_pregroupoid_iso_comma _ _ (pr2 C₁) (pr2 C₂)). - refine (_ ,, tt). apply iso_comma_pr1. - refine (_ ,, tt). apply iso_comma_pr2. - use make_invertible_2cell. + refine (_ ,, tt). apply iso_comma_commute. + apply locally_groupoid_grpds. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Examples.Groupoids. Require Import UniMath.Bicategories.Limits.Pullbacks.