Definition opcartesian_factorisation_disp_functor_data : disp_functor_data G D₁ D₂. Proof. simple refine (_ ,, _). - exact (λ x xx, ob_of_opcartesian_lift _ (HD₁ (F x) (G x) (FF x xx) (α x))). - exact (λ x y xx yy f ff, opcartesian_factorisation (mor_of_opcartesian_lift_is_opcartesian _ (HD₁ (F x) (G x) (FF x xx) (α x))) _ (transportf (λ z, _ -->[ z ] _) (nat_trans_ax α _ _ f) (♯ FF ff ;; mor_of_opcartesian_lift _ (HD₁ (F y) (G y) (FF y yy) (α y))))). 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.