Definition is_opcartesian_z_iso_disp {C : category} {D : disp_cat C} {x : C} {xx : D x} {y : C} {yy : D y} {f : x --> y} {Hf : is_z_isomorphism f} {ff : xx -->[ f ] yy} (Hff : is_z_iso_disp (make_z_iso' f Hf) ff) : is_opcartesian ff. Proof. apply is_cartesian_to_is_opcartesian. use (@is_cartesian_z_iso_disp _ (op_disp_cat D) _ _ _ _ _ _ ff). - exact (pr2 (@opp_z_iso C _ _ (make_z_iso' f Hf))). - use (@to_z_iso_disp_op_disp_cat C D y x (make_z_iso' f Hf) yy xx ff). exact Hff. Defined.
Require Import UniMath.Foundations.Sets. 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.Categories.HSET.Core. Require Import UniMath.CategoryTheory.Categories.HSET.MonoEpiIso. Require Import UniMath.CategoryTheory.Categories.HSET.Univalence. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.NaturalTransformations. Require Import UniMath.CategoryTheory.DisplayedCats.Fiber. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Opposite. Section IsoCleavingFromOpcleaving. End IsoCleavingFromOpcleaving.