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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- implicit val F: Functor[F]
- implicit val G: Functor[G]
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- 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 -| Gis an adjunction, andP -| Qis 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.
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- def leftAdjunct[A, B](a: => A)(f: (F[A]) => B): G[B]
Every
F-algebra maps to aG-coalgebra. - implicit val monad: Monad[[α]G[F[α]]]
Every adjunction gives rise to a monad.
- final def ne(arg0: AnyRef): Boolean
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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 anF-algebra. - final def synchronized[T0](arg0: => T0): T0
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- def unit[A](a: => A): G[F[A]]
Puts a value into the monad.
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- implicit val zapFG: Zap[F, G]
Adjoint functors annihilate each other.
- implicit val zapGF: Zap[G, F]
Adjoint functors annihilate each other.