Definition ptset_disp_cat : disp_cat SET. Proof. use disp_struct. - exact (λ X, pr1 X). - exact (λ _ _ m n f, preserve_ptset m n f). - intros x y m n f. apply isaprop_preserve_ptset. - intros X x. apply id_preserve_ptset. - intros X Y Z f g x y z pf pg. apply (comp_preserve_ptset pf pg). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Monoidal.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.DisplayedCartesianMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Import DisplayedBifunctorNotations.