CatT.scala

// From Conceptual Mathematics and http://eed3si9n.com/learning-scalaz/Category+theory.html

sealed trait Person {}
case object John extends Person {}
case object Mary extends Person {}
case object Sam extends Person {}

val a: Set[Person] = Set[Person](John, Mary, Sam)

sealed trait Breakfast {}
case object Eggs extends Breakfast {}
case object Oatmeal extends Breakfast {}
case object Toast extends Breakfast {}
case object Coffee extends Breakfast {}

sealed trait Dish {}
case object Mug extends Dish {}
case object Plate extends Dish {}
case object Bowl extends Dish {}

val favoriteBreakfast: Person => Breakfast = {
  case John => Eggs
  case Mary => Coffee
  case Sam  => Coffee
}

val favoritePerson: Person => Person = {
  case John => Mary
  case Mary => John
  case Sam  => Mary
}

val servedIn: Breakfast => Dish = {
  case Eggs => Plate
  case Coffee => Mug
  case Oatmeal => Bowl
  case Toast => Plate
}
       
val favoritePersonsBreakfast = favoriteBreakfast compose favoritePerson
val favoritePersonsBreakfastDish = servedIn compose favoriteBreakfast compose favoritePerson