Definition orthogonal_via_pb_cone (HB_2_1 : is_univalent_2_1 B) : @pb_cone bicat_of_univ_cats (univ_hom HB_2_1 b₁ c₁) (univ_hom HB_2_1 b₂ c₂) (univ_hom HB_2_1 b₁ c₂) (post_comp b₁ g) (pre_comp c₂ f). Proof. use make_pb_cone. - exact (univ_hom HB_2_1 b₂ c₁). - exact (pre_comp c₁ f). - exact (post_comp b₂ g). - use nat_z_iso_to_invertible_2cell. exact (pre_comp_post_comp_commute_z_iso f g). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful. Require Import UniMath.CategoryTheory.IsoCommaCategory. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.Bicategories.Morphisms.Properties.ClosedUnderInvertibles. Require Import UniMath.Bicategories.Limits.Pullbacks. Require Import UniMath.Bicategories.Limits.PullbackFunctions. Import PullbackFunctions.Notations. Require Import UniMath.Bicategories.Limits.PullbackEquivalences. Require Import UniMath.Bicategories.Limits.Examples.BicatOfUnivCatsLimits.