Definition is_sym_monoidal_adjunction {C₁ C₂ : category} {M₁ : monoidal C₁} {M₂ : monoidal C₂} (S₁ : symmetric M₁) (S₂ : symmetric M₂) {A : adjunction C₁ C₂} (HA : monoidal_adjunction M₁ M₂ A) : UU := is_symmetric_monoidal_functor S₁ S₂ (fmonoidal_lax_left_adjoint HA) × is_symmetric_monoidal_functor S₂ S₁ (fmonoidal_lax_right_adjoint HA).
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.