Definition disp_functor_over_pair_inv_data {C : category} {D₁ D₂ : disp_cat (category_binproduct C C)} (F : disp_functor (pair_functor (functor_identity C) (functor_identity C)) D₁ D₂) : disp_functor_data (functor_identity (category_binproduct C C)) D₁ D₂. Proof. simple refine (_ ,, _). - exact (λ x xx, F x xx). - exact (λ x y f xx yy ff, ♯F ff)%mor_disp. Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors.