Proposition is_symmetric_lift_poset_comonad : is_symmetric_monoidal_functor (pr21 pointed_poset_sym_mon_closed_cat) (pr21 pointed_poset_sym_mon_closed_cat) lax_monoidal_lift_poset_comonad. Proof. intros X Y. use eq_mor_hset_struct. use setquotunivprop' ; [ intro ; apply setproperty | ]. intros xy. induction xy as [ x y ]. induction x as [ x | ] ; induction y as [ y | ] ; apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.Posets. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.CartesianStructure. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructureLimitsAndColimits. Require Import UniMath.CategoryTheory.DisplayedCats.Structures.StructuresSmashProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.PointedPosetStrict. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.FunctorCategories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Monoidal.Examples.SmashProductMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.PosetsMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.CategoryOfPosets. Require Import UniMath.CategoryTheory.Monads.Comonads. Require Import UniMath.CategoryTheory.Monoidal.Comonoids.Category.