Definition opp_is_z_isomorphism {C : precategory} {a b : C} (f : a --> b) : @is_z_isomorphism C a b f -> @is_z_isomorphism C^op b a f. Proof. intros H. use make_is_z_isomorphism. - exact (is_z_isomorphism_mor H). - exact (opp_is_inverse_in_precat (is_inverse_in_precat_inv H)). Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.FunctorCategory.