Lemma symmetric_monoidal_comonad_category_Pisset (smF : ∑ (F : C ⟶ C) (d : fmonoidal_lax M M F), is_symmetric_monoidal_functor HM HM d) : isaset (∑ H : ∑ T : disp_Comonad_data (pr1 smF), disp_Comonad_laws T, symmetric_monoidal_comonads_extra_laws (pr12 smF) (pr11 H) (pr21 H)). Proof. change isaset with (isofhlevel 2). apply isofhleveltotal2. - apply isofhleveltotal2. { apply isasetdirprod; apply [C,C]. } intro T. apply isasetaprop. apply isaprop_disp_Comonad_laws. - intro TT. apply isasetaprop. apply isaprop_symmetric_monoidal_comonads_extra_laws. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Sigma. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Monads.Comonads.