Definition op_z_iso_is_cat_z_iso {C : category} (X Y : C^op) : @z_iso C Y X ≃ z_iso X Y. Proof. use weqfibtototal. intro f. use weqimplimpl. - apply opp_is_z_isomorphism. - apply z_iso_from_opp. - apply isaprop_is_z_isomorphism. - apply (isaprop_is_z_isomorphism(C:=op_category C)). 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.