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trait Lan[G[_], H[_], A] extends AnyRef

The left Kan extension of H along G

Self Type
Lan[G, H, A]
Source
Kan.scala
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Type Members

  1. abstract type I

Abstract Value Members

  1. abstract def f(gi: G[I]): A
  2. abstract def v: H[I]

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
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  2. final def ##: Int
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  3. final def ==(arg0: Any): Boolean
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  4. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
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    protected[lang]
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    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  6. final def eq(arg0: AnyRef): Boolean
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  7. def equals(arg0: AnyRef): Boolean
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  8. def finalize(): Unit
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    protected[lang]
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    @throws(classOf[java.lang.Throwable])
  9. final def getClass(): Class[_ <: AnyRef]
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    @native()
  10. def hashCode(): Int
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    @native()
  11. final def isInstanceOf[T0]: Boolean
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  12. def map[B](g: (A) => B): Lan[G, H, B]
  13. final def ne(arg0: AnyRef): Boolean
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  14. final def notify(): Unit
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    @native()
  15. final def notifyAll(): Unit
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    @native()
  16. final def synchronized[T0](arg0: => T0): T0
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  17. def toAdjoint[F[_]](implicit H: Functor[H], A: Adjunction[G, F]): H[F[A]]

    If G is left adjoint to F, there is a natural isomorphism between Lan[G,H,_] and H[F[_]]

  18. def toLan[F[_]](s: ~>[H, [α]F[G[α]]])(implicit arg0: Functor[F]): F[A]

    The universal property of a left Kan extension.

    The universal property of a left Kan extension. The functor Lan[G,H,_] and the natural transformation glan[G,H,_] are universal in the sense that for any functor F and a natural transformation s from H to F[G[_]], a unique natural transformation toLan exists from Lan[G,H,_] to F such that for all h, glan(h).toLan = s(h).

  19. def toString(): String
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  20. final def wait(): Unit
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    @throws(classOf[java.lang.InterruptedException])
  21. final def wait(arg0: Long, arg1: Int): Unit
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    @throws(classOf[java.lang.InterruptedException])
  22. final def wait(arg0: Long): Unit
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    @throws(classOf[java.lang.InterruptedException]) @native()

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