Definition opp_z_iso {C : precategory} {a b : C} : @z_iso C a b -> @z_iso C^op b a. Proof. intros H. use make_z_iso. - exact (z_iso_mor H). - exact (inv_from_z_iso 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.