let kCat = ../Cat/semigroupal

let vObject = Type

in  λ(object : Kind) →
    λ(v : ./Kind kCat Type vObject) →
    λ(cat : ./Kind kCat vObject object) →
      let Set =
            ./Cartesian/extractMonoidal
              kCat
              vObject
              Type
              ../Set/monoidal/cartesian

      let vBase = ./extractCategory kCat Type vObject v

      in    { CommutativeGroup = ../../Group/Commutative/Type object cat
            , CommutativeMonoid = ../../Monoid/Commutative/Type object cat
            , Day = ../../Day/Type object Set cat
            , Field = ../../Field/Type object cat
            , Group = ../../Group/Type object cat
            , Monoid = ../../Monoid/Type object cat
            , MonoidalFunctor = ../../Functor/Monoidal/Type object vBase cat Set
            , Rig = ../../Rig/Type object cat
            , Ring = ../../Ring/Type object cat
            , Semiring = ../../Semiring/Type object cat
            , StrongFunctor = ../../Functor/Strong/Type object vBase cat
            }
          ∧ ../Semigroupal/types.dhall
              object
              v
              (./extractSemigroupal kCat vObject object cat)