Definition op_is_univalent (C : univalent_category) : is_univalent (op_category C). Proof. intros X Y. use weqhomot. + exact ((op_z_iso_is_cat_z_iso X Y) ∘ make_weq (@idtoiso C Y X) (pr2( C) Y X) ∘ weqpathsinv0 _ _)%weq. + intros p. induction p ; cbn. apply subtypePath. * intro ; apply (isaprop_is_z_isomorphism(C:=op_category C)). * apply idpath. 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.