Definition monoidal_adjunction {C₁ C₂ : category} (M₁ : monoidal C₁) (M₂ : monoidal C₂) (A : adjunction C₁ C₂) (L := left_adjoint A : C₁ ⟶ C₂) (R := right_adjoint A : C₂ ⟶ C₁) (η := adjunit A) (ε := adjcounit A) : UU := ∑ (HL : fmonoidal_lax M₁ M₂ L), ∑ (HR : fmonoidal_lax M₂ M₁ R), is_mon_nat_trans (identity_fmonoidal _) (comp_fmonoidal_lax HL HR) η × is_mon_nat_trans (comp_fmonoidal_lax HR HL) (identity_fmonoidal _) ε.
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.