Definition sym_monoidal_adjunction_to_sym_monoidal_cmd {V₁ V₂ : sym_monoidal_cat} (A : adjunction V₁ V₂) (HA : sym_monoidal_adjunction V₁ V₂ A) : sym_monoidal_cmd V₂. Proof. use make_symmetric_monoidal_comonad. - exact (Comonad_from_adjunction A). - exact (comp_fmonoidal_lax (fmonoidal_lax_right_adjoint HA) (fmonoidal_lax_left_adjoint HA)). - exact (is_symmetric_monoidal_comp (is_symmetric_monoidal_functor_right_adjoint HA) (is_symmetric_monoidal_functor_left_adjoint HA)). - exact (sym_monoidal_adjunction_to_sym_monoidal_cmd_comult A HA). - exact (monoidal_adjcounit HA). Defined.
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.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monads.Comonads. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Monoidal.FunctorCategories. 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. Import BifunctorNotations. Import MonoidalNotations. Section MonoidalAdjunctionFromStrong. End MonoidalAdjunctionFromStrong. Section SymMonoidalAdjunctionFromStrong. End SymMonoidalAdjunctionFromStrong.