proposition: Lemma eilenberg_moore_cmd_form_adj : form_adjunction' (eilenberg_moore_forget,, eilenberg_moore_cofree,, eilenberg_moore_adj_unit,, ε (linear_category_bang 𝕃)).
proof: Proof. split. - exact (λ x, pr12 x). - intro x. use eq_mor_co_eilenberg_moore. cbn. refine (assoc' _ _ _ @ _). refine (id_left _ @ _). exact (Comonad_law2 (T := linear_category_bang 𝕃) x). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Adjunctions UniMath.CategoryTheory.Monoidal.FunctorCategories UniMath.CategoryTheory.Monoidal.Structure.Cartesian UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Categories.CoEilenbergMoore UniMath.CategoryTheory.Monoidal.Examples.MonoidalDialgebras UniMath.CategoryTheory.Monoidal.Examples.SymmetricMonoidalCoEilenbergMoore UniMath.Semantics.LinearLogic.LinearCategory