What does suffix -al convey in Semigroupal in contrast to Semigroup?

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There exist Semigroup and Semigrupal

Semigroup[Int].combine(1, 41)                  // : Int = 42
Semigroupal[Option].product(Some(1), Some(41)) // : Option[(Int, Int)] = Some(value = (1, 41))

What is -al suffix meant to convey? In what sense does -al convey the distinction between Semigroup and Semigroupal? Similarly there is language of Monoid and Monoidal; is -al here conveying the distinction along the same lines?

scala-cats scala terminology
2 Answers

edmundnoble states semigroupal is an abbreviation

Semigroupal is an abbreviation for semigroupal functor which is to a monoidal functor as a semigroup is to a monoid

or as hrhino puts it

"semigroupal functor" - "functor" = "semigroupal"

cats.Semigroupal points towards the concept of semigroupal functor which is defined something like

trait SemigroupalFunctor[F[_]] {
  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
  def map[A, B](fa: F[A])(f: A => B): F[B]
}

semigroupal functor is like monoidal functor without the unit

trait MonoidalFunctor[F[_]] {
  def unit: F[Unit]
  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
  def map[A, B](fa: F[A])(f: A => B): F[B]
}

Now cats.Semigroupal is a generalisation of semigroupal functor where only the product is extracted into its own type class

trait Semigroupal[F[_]] {
  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
}

hence the naming stops at just Semigroupal instead of SemigroupalFunctor. The full semigroupal functor can be found in cats in the form of Apply which combines Semigroupal and Functor as shown in the following simplified view

trait Semigroupal[F[_]] {
  def product[A, B](fa: F[A], fb: F[B]): F[(A, B)]
}

trait Functor[F[_]] {
  def map[A, B](fa: F[A])(f: A => B): F[B]
}

trait Apply[F[_]] extends Semigroupal[F] with Functor[F] { 
  def ap[A, B](ff: F[A => B])(fa: F[A]): F[B]
}

Semigroupal used to be called Cartesian until rename Cartesian to Semigroupal #1961

user_52050220

See this paper on semigroupal categories. I don't believe a Semigroupal has to actually represent a semigroupal category, but its product operation is something semigroupal categories have as well.

Similarly there is language of Monoid and Monoidal; is -al here conveying the distinction along the same lines?

Yes, it's related in the same way (but monoidal categories seem to be much more widely used).

alexey_r_92040
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