proposition: Proposition linear_category_comult_preserves_tensor (x y : 𝕃) : mon_functor_tensor (linear_category_bang_functor 𝕃) x y · linear_category_comult 𝕃 (x ⊗ y) = (linear_category_comult 𝕃 x) #⊗ (linear_category_comult 𝕃 y) · (inner_swap 𝕃 (linear_category_bang 𝕃 x) (linear_category_bang 𝕃 x) (linear_category_bang 𝕃 y) (linear_category_bang 𝕃 y) · mon_functor_tensor (linear_category_bang_functor 𝕃) x y #⊗ mon_functor_tensor (linear_category_bang_functor 𝕃) x y).
proof: Proof. exact (pr12 (pr222 (pr222 (pr222 𝕃))) x y). Qed.
imports: UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Monads.Comonads UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.FunctorCategories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Monoidal.Structure.SymmetricDiagonal UniMath.CategoryTheory.Monoidal.Structure.Closed UniMath.CategoryTheory.Monoidal.Comonoids.Category UniMath.CategoryTheory.Monoidal.Examples.ConstantFunctor UniMath.CategoryTheory.Monoidal.CategoriesOfMonoids UniMath.CategoryTheory.Categories.Dialgebras UniMath.CategoryTheory.Monoidal.Examples.DiagonalFunctor