Adjunction

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

Linear Supertypes

AnyRef, Any

Instance Constructors

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

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
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final def ==(arg0: Any): Boolean

Definition Classes
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implicit val F: Functor[F]
implicit val G: Functor[G]
final def asInstanceOf[T0]: T0

Definition Classes
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def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( ... )
implicit val comonad: Comonad[[α]F[G[α]]]

Every adjunction gives rise to a comonad.
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.
def counit[A](a: F[G[A]]): A

Extracts a value out of the comonad.
final def eq(arg0: AnyRef): Boolean

Definition Classes
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def equals(arg0: Any): Boolean

Definition Classes
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def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
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Annotations
@throws( classOf[java.lang.Throwable] )
final def getClass(): Class[_]

Definition Classes
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def hashCode(): Int

Definition Classes
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final def isInstanceOf[T0]: Boolean

Definition Classes
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def leftAdjunct[A, B](a: ⇒ A)(f: (F[A]) ⇒ B): G[B]

Every F-algebra maps to a G-coalgebra.
implicit val monad: Monad[[α]G[F[α]]]

Every adjunction gives rise to a monad.
final def ne(arg0: AnyRef): Boolean

Definition Classes
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final def notify(): Unit

Definition Classes
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final def notifyAll(): Unit

Definition Classes
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implicit val representable: Representable[G, F[Unit]]

Every adjunction is representable.
def rightAdjunct[A, B](a: F[A])(f: (A) ⇒ G[B]): B

Every G-coalgebra maps to an F-algebra.
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
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def toString(): String

Definition Classes
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def unit[A](a: ⇒ A): G[F[A]]

Puts a value into the monad.
final def wait(): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
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Annotations
@throws( ... )
final def wait(arg0: Long): Unit

Definition Classes
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Annotations
@throws( ... )
implicit val zapFG: Zap[F, G]

Adjoint functors annihilate each other.
implicit val zapGF: Zap[G, F]

Adjoint functors annihilate each other.

Related Docs: object Adjunction | package scalaz

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

Instance Constructors

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

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

implicit val F: Functor[F]

implicit val G: Functor[G]

final def asInstanceOf[T0]: T0

def clone(): AnyRef

implicit val comonad: Comonad[[α]F[G[α]]]

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

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

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def leftAdjunct[A, B](a: ⇒ A)(f: (F[A]) ⇒ B): G[B]

implicit val monad: Monad[[α]G[F[α]]]

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

implicit val representable: Representable[G, F[Unit]]

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

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

def unit[A](a: ⇒ A): G[F[A]]

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

implicit val zapFG: Zap[F, G]

implicit val zapGF: Zap[G, F]

Inherited from AnyRef

Inherited from Any

Ungrouped