Definition is_opcartesian_comp_disp {C : category} {D : disp_cat C} {x : C} {xx : D x} {y : C} {yy : D y} {z : C} {zz : D z} {f : x --> y} {g : y --> z} {ff : xx -->[ f ] yy} {gg : yy -->[ g ] zz} (Hff : is_opcartesian ff) (Hgg : is_opcartesian gg) : is_opcartesian (ff ;; gg)%mor_disp. Proof. apply is_cartesian_to_is_opcartesian. use (@is_cartesian_comp_disp _ (op_disp_cat D)). - apply is_opcartesian_weq_is_cartesian. exact Hgg. - apply is_opcartesian_weq_is_cartesian. 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.