Definition binary_coproducts_struct_poset : hset_binary_coprod_struct struct_poset. Proof. simple refine (_ ,, _). - exact (λ X Y PX PY, coproduct_PartialOrder PX PY). - simple refine (_ ,, _ ,, _) ; cbn. + abstract (intros X Y PX PY ; cbn ; exact (is_monotone_inl PX PY)). + abstract (intros X Y PX PY ; cbn ; exact (is_monotone_inr PX PY)). + abstract (intros X Y Z PX PY PZ f g Pf Pg ; exact (is_monotone_sumofmaps _ _ Pf Pg)). 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.