Definition orthogonal_functor {B : bicat} {b₁ b₂ : B} (f : b₁ --> b₂) {c₁ c₂ : B} (g : c₁ --> c₂) : hom b₂ c₁ ⟶ iso_comma (post_comp b₁ g) (pre_comp c₂ f). Proof. use iso_comma_ump1. - exact (pre_comp c₁ f). - exact (post_comp b₂ g). - 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.