Definition poset_disp_cat : disp_cat SET. Proof. use disp_struct. - exact (λ X, PartialOrder X). - exact (λ X₁ X₂ R₁ R₂ f, is_monotone R₁ R₂ f). - exact (λ X₁ X₂ R₁ R₂ f, isaprop_is_monotone R₁ R₂ f). - exact (λ X R, idfun_is_monotone R). - exact (λ X₁ X₂ X₃ R₁ R₂ R₃ f g Hf Hg, comp_is_monotone Hf Hg). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.exponentials. Require Import UniMath.CategoryTheory.Categories.HSET.All.