Definition is_univalent_op_disp_cat {C : category} {D : disp_cat C} (HD : is_univalent_disp D) : is_univalent_disp (op_disp_cat D). Proof. intros x y p xx yy. induction p. use weqhomot. - exact (z_iso_disp_weq_op_disp_cat xx yy ∘ make_weq _ (HD x x (idpath _) xx yy))%weq. - abstract (intro p ; use subtypePath ; [ intro ; apply isaprop_is_z_iso_disp | ] ; induction p ; cbn ; apply idpath). Defined.
Require Import UniMath.Foundations.All. 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.opp_precat. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence.