let kCat = ../Category/Cat/semigroupal

let Set = ../Category/Set/rig

let vObject = Type

let v =
      ../Category/Monoidal/Cartesian/extractCategory
        kCat
        Type
        vObject
        ../Category/Set/monoidal/cartesian

let object = Type

let cat = ../Category/Rig/extractMultiplicative kCat vObject object Set

let CommutativeSemigroup =
      ../Semigroup/Commutative/Type
        object
        (../Category/Monoidal/extractSemigroupal kCat vObject object cat)

let extractMonoid = ../Functor/Monoidal/extractMonoid object v cat cat

in  λ(a : object) →
    λ(semigroup : CommutativeSemigroup a) →
        { additive =
            extractMonoid
              (λ(b : object) → Set.additive.product { _1 = a, _2 = b })
              (./functor/monoidal/parallel a semigroup)
        , multiplicative =
            extractMonoid
              (λ(b : object) → Set.additive.product { _1 = a, _2 = b })
              (./functor/monoidal/sequential a)
        }
      : ../Duoid/Type
          (kCat.arrow object object)
          (../Category/Endofunctor/monoidal/functor v cat)
          (λ(b : object) → Set.additive.product { _1 = a, _2 = b })