Reference: http://eed3si9n.com/herding-cats/initial.html

Note that category set forms semiring with product and coproduct, so it makes sens to name some of its objects as 0 and 1. Further reading: https://github.com/mtumilowicz/scala212-category-theory-set-semiring

In any category C, an object

• 0 is initial if for any object c e C there is exactly one isomorphism 0 -> c
• 1 is terminal if for any object c e C there is exactly one isomorphism c -> 1

Remark: initial (terminal) objects are unique up to isomorphism.

We will provide implementation of initial and terminal object in set category.

In Sets, the empty set is initial and any singleton set is terminal.

We take uninhabited type Nothing and we provide implementation of absurd function (https://hackage.haskell.org/package/void-0.6.1/docs/Data-Void.html).

def absurd[A]: Nothing => A = _ => ???

• it cannot be called
• it exists

  val obj = TerminalObjects
  obj.absurd[Int] should not be null
  

We take singleton set Unit, there can be only one implementation of function between Unit and A

def unit[A](a: A): Unit = ()

test("single unit function") {
  val obj = TerminalObjects
  obj.unit(1) should be (obj.unit(2))
}