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abstract class Adjunction[F[_], G[_]] extends AnyRef

An adjunction formed by two functors F and G such that F is left-adjoint to G. The composite functor GF is a monad and the composite functor FG is a comonad.

The minimal definition is either (unit, counit) or (leftAdjunct, rightAdjunct)

Self Type
Adjunction[F, G]
Source
Adjunction.scala
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Instance Constructors

  1. new Adjunction()(implicit F: Functor[F], G: Functor[G])

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
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  2. final def ##(): Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
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  4. implicit val F: Functor[F]
  5. implicit val G: Functor[G]
  6. final def asInstanceOf[T0]: T0
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  7. def clone(): AnyRef
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    protected[lang]
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    @throws( ... ) @native()
  8. implicit val comonad: Comonad[[α]F[G[α]]]

    Every adjunction gives rise to a comonad.

  9. def compose[P[_], Q[_]](implicit A: -|[P, Q]): -|[[α]P[F[α]], [α]G[Q[α]]]

    Adjunctions compose in a natural fashion.

    Adjunctions compose in a natural fashion. If F -| G is an adjunction, and P -| Q is an adjunction, then PF -| GQ is an adjunction. In fact, adjunctions in Scala form a monoid.

  10. def counit[A](a: F[G[A]]): A

    Extracts a value out of the comonad.

  11. final def eq(arg0: AnyRef): Boolean
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  12. def equals(arg0: Any): Boolean
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  13. def finalize(): Unit
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    protected[lang]
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    @throws( classOf[java.lang.Throwable] )
  14. final def getClass(): Class[_]
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    @native()
  15. def hashCode(): Int
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    @native()
  16. final def isInstanceOf[T0]: Boolean
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  17. def leftAdjunct[A, B](a: ⇒ A)(f: (F[A]) ⇒ B): G[B]

    Every F-algebra maps to a G-coalgebra.

  18. implicit val monad: Monad[[α]G[F[α]]]

    Every adjunction gives rise to a monad.

  19. final def ne(arg0: AnyRef): Boolean
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  20. final def notify(): Unit
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    @native()
  21. final def notifyAll(): Unit
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    @native()
  22. implicit val representable: Representable[G, F[Unit]]

    Every adjunction is representable.

  23. def rightAdjunct[A, B](a: F[A])(f: (A) ⇒ G[B]): B

    Every G-coalgebra maps to an F-algebra.

  24. final def synchronized[T0](arg0: ⇒ T0): T0
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  25. def toString(): String
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  26. def unit[A](a: ⇒ A): G[F[A]]

    Puts a value into the monad.

  27. final def wait(): Unit
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    @throws( ... )
  28. final def wait(arg0: Long, arg1: Int): Unit
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    @throws( ... )
  29. final def wait(arg0: Long): Unit
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  30. implicit val zapFG: Zap[F, G]

    Adjoint functors annihilate each other.

  31. implicit val zapGF: Zap[G, F]

    Adjoint functors annihilate each other.

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