Definition set_coproducts_struct_poset (I : hSet) : hset_struct_set_coprod struct_poset I. Proof. simple refine (_ ,, _). - exact (λ Y PY, coproduct_set_PartialOrder _ PY). - simple refine (_ ,, _) ; cbn. + abstract (intros Y PY ; cbn ; exact (is_monotone_set_in _ PY)). + abstract (refine (λ Y PY W PW f Pf, _) ; exact (is_monotone_set_coproduct_map _ _ Pf)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits.