{-|

**NB**: This is defined in terms of the monoidal categories instead of the other
way around because this is more restrictive than either monoidal category.
- Applicative requires that the target category is **Set** and
- monadic requires an endofunctor`object`.

When you combine these two restrictions, you end up only being able to support
endofunctors in **Set**.
-}
let kCat = ../Cat/semigroupal

let vObject = Type

let object = Type

in  λ(v : ../../Category/Kind kCat Type vObject) →
    λ(cat : ../../Category/Monoidal/Kind kCat vObject object) →
      let applicative = ../Functor/monoidal object v cat cat

      let monadic =
            ./monoidal/monadic
              object
              v
              (../../Category/Monoidal/extractCategory kCat vObject object cat)

      in    { constraint = monadic.constraint
            , arrow = applicative.arrow
            , diamond =
              { unit = applicative.unit, product = applicative.product }
            , star = { unit = monadic.unit, product = monadic.product }
            }
          : ../Duoidal/Kind kCat vObject (kCat.arrow object object)