Definition right_adjoint_monoidal_data_from_strong : fmonoidal_data M₂ M₁ R. Proof. simple refine (_ ,, _). - intros x y. exact (η _ · #R (inv_from_z_iso (_ ,, fmonoidal_preservestensorstrongly HL (R x) (R y)) · (ε x ⊗^{M₂} ε y))). - exact (η _ · #R (inv_from_z_iso (_ ,, fmonoidal_preservesunitstrongly HL))). 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.