Definition discrete_twosided_disp_cat_is_fibration {C₁ C₂ : category} {D : twosided_disp_cat C₁ C₂} (HD : discrete_twosided_disp_cat D) (HD' : is_discrete_twosided_fibration HD) : twosided_fibration D. Proof. simple refine (_ ,, _ ,, _). - apply discrete_twosided_disp_cat_to_opcleaving. + exact HD. + apply HD'. - apply discrete_twosided_disp_cat_to_cleaving. + exact HD. + apply HD'. - cbn. unfold is_iso_twosided_commute. intro ; intros. apply HD. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete.