Definition twosided_disp_cat_to_disp_cat_id_comp (D : twosided_disp_cat C₁ C₂) : disp_cat_id_comp (category_binproduct C₁ C₂) (twosided_disp_cat_to_disp_cat_ob_mor D). Proof. simple refine (_ ,, _). - exact (λ xy z, id_two_disp z). - exact (λ xy₁ xy₂ xy₃ fg₁ fg₂ z₁ z₂ z₃ h₁ h₂, h₁ ;;2 h₂). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.