Definition op_iso_is_cat_iso {C : category} (X Y : C^op) : @iso C Y X ≃ iso X Y. Proof. use weqfibtototal. intro f. use weqimplimpl. - apply opp_is_iso. - apply iso_from_opp. - apply isaprop_is_iso. - apply isaprop_is_iso. 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.