proposition: Lemma leftclosed_symmetric_is_rightclosed {C : category} (M : monoidal C) : symmetric M -> monoidal_leftclosed M -> monoidal_rightclosed M.
proof: Proof. intros B LC. intro x. exists (monoidal_leftclosed_exp LC x). apply (adj_closed_under_nat_z_iso (F2 := rightwhiskering_functor M x)). - apply symmetric_whiskers_swap_nat_z_iso. exact B. - exact (pr2 (LC x)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric