Definition twosided_disp_cat_product_iso_weq_map {wx : category_binproduct C₁ C₂} {yz : category_binproduct C₃ C₄} {d₁ d₂ : twosided_disp_cat_product_data wx yz} (fg : iso_twosided_disp (identity_z_iso (pr1 wx)) (identity_z_iso (pr1 yz)) (pr1 d₁) (pr1 d₂)) (hk : iso_twosided_disp (identity_z_iso (pr2 wx)) (identity_z_iso (pr2 yz)) (pr2 d₁) (pr2 d₂)) : @iso_twosided_disp _ _ twosided_disp_cat_product _ _ _ _ (identity_z_iso wx) (identity_z_iso yz) d₁ d₂. Proof. use make_iso_twosided_disp. - exact (pr1 fg ,, pr1 hk). - apply is_isotwosided_disp_twosided_disp_cat_product. + apply fg. + apply hk. Defined.
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.Core.Univalence. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.