org.specs2.internal.scalaz

Category

object Category

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  1. trait <*>[F[_], G[_]] extends AnyRef

  2. case class <=[A, B](value: (B) ⇒ A) extends NewType[(B) ⇒ A] with Product with Serializable

    The flipped Function1 type

  3. type <=>[A, B] = Iso[Function1, A, B]

    Set isomorphism

  4. type <~>[F[_], G[_]] = Iso2[~>, F, G]

    Natural isomorphism between functors

  5. type <~~>[F[_, _], G[_, _]] = Iso3[~~>, F, G]

    Isomorphism natural in both sides of a bifunctor

  6. type Adjunction[F[_], U[_]] = Iso3[~~>, [A, B](F[A]) ⇒ B, [A, B](A) ⇒ U[B]]

  7. type Alpha[Arr[_, _], X, Y] = ~>[[α]Arr[α, X], [α]Arr[α, Y]]

  8. case class Compose[F[_], G[_], Arr[_, _], X](value: F[G[X]]) extends NewType[F[G[X]]] with Product with Serializable

    Functor composition

  9. case class Discrete[X, A, B](value: (X) ⇒ X) extends NewType[(X) ⇒ X] with Product with Serializable

  10. type GeneralAdjunction[P[_, _], Q[_, _], F[_], U[_]] = Iso3[~~>, [A, B]P[F[A], B], [A, B]Q[A, U[B]]]

  11. trait GeneralizedContravariant[C[_, _], D[_, _], F[_]] extends AnyRef

  12. trait GeneralizedFunctor[C[_, _], D[_, _], F[_]] extends AnyRef

    A Functor that is not necessarily an endofunctor in the Scala category.

  13. case class Iso[Arr[_, _], A, B](to: Arr[A, B], from: Arr[B, A]) extends Product with Serializable

    Isomorphism for arrows of kind * -> * -> *

  14. case class Iso2[Arr[_[_], _[_]], F[_], G[_]](to: Arr[F, G], from: Arr[G, F]) extends Product with Serializable

    Isomorphism for arrows of kind (* -> *) -> (* -> *) -> *

  15. case class Iso3[Arr[_[_, _], _[_, _]], F[_, _], G[_, _]](to: Arr[F, G], from: Arr[G, F]) extends Product with Serializable

    Isomorphism for arrows of kind (* -> * -> *) -> (* -> * -> *) -> *

  16. sealed class MonoidCategory[M] extends GeneralizedCategory with Hom

  17. trait Nat[Arr[_, _], F[_], G[_]] extends AnyRef

    Generalized natural transformations

  18. sealed class Ord2[X, A, B] extends AnyRef

  19. sealed trait P[+IX, +IY] extends AnyRef

    Index for a product category

  20. case class ProductCategory[UX <: Hom, UY <: Hom](_1: GeneralizedCategory { type U = UX }, _2: GeneralizedCategory { type U = UY }) extends GeneralizedCategory with Hom with Product with Serializable

  21. trait Reader[R] extends AnyRef

  22. trait Writer[R] extends AnyRef

Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
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  2. final def !=(arg0: Any): Boolean

    Definition Classes
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  3. final def ##(): Int

    Definition Classes
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  4. implicit val <:<_Category: Category[<:<]

  5. implicit val =:=_Category: Category[=:=]

  6. final def ==(arg0: AnyRef): Boolean

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

    Definition Classes
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  8. implicit def CokleisliCategory[M[_]](implicit arg0: Comonad[M]): Category[[α, β]Cokleisli[M, α, β]]

  9. implicit def ComposeContravariants[F[_], G[_]](implicit arg0: Contravariant[F], arg1: Contravariant[G]): Functor[[X]Compose[F, G, <=, X]]

    Compose contravariants

  10. implicit def ComposeFunctors[F[_], G[_]](implicit arg0: Functor[F], arg1: Functor[G]): Functor[[X]Compose[F, G, Function1, X]]

    Compose functors

  11. implicit def DiscreteCategory[X]: Category[[α, β]Discrete[X, α, β]]

    Discrete categories, whose only morphism is the identity function.

    Discrete categories, whose only morphism is the identity function. *

  12. implicit val Function1Category: Category[Function1]

    The Set category *

  13. implicit def KleisliCategory[M[_]](implicit arg0: Monad[M]): Category[[α, β]Kleisli[M, α, β]]

  14. implicit def MorphismToObject[A, B, C](a: Const2[A, B, C]): A

  15. implicit def ObjectToMorphism[A, B, C](a: A): Const2[A, Unit, Unit]

  16. implicit val OpCategory: Category[<=]

    The opposite category of the Set category.

  17. implicit def PartialFunctionCategory: Category[PartialFunction]

  18. implicit def PosetCategory[X](implicit arg0: Order[X]): Category[[α, β]Ord2[X, α, β]]

    Every partial order gives rise to a category *

  19. final def asInstanceOf[T0]: T0

    Definition Classes
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  20. def clone(): AnyRef

    Attributes
    protected[java.lang]
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    @throws()

  21. def contravariantInScala[F[_]](f: Contravariant[F]): GeneralizedFunctor[<=, Function1, F]

  22. def endoFunctorInScala[F[_]](f: Functor[F]): GeneralizedFunctor[Function1, Function1, F]

  23. final def eq(arg0: AnyRef): Boolean

    Definition Classes
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  24. def equals(arg0: Any): Boolean

    Definition Classes
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  25. def finalize(): Unit

    Attributes
    protected[java.lang]
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  26. implicit def flipFunctorIso[F[_], G[_]](implicit i: <~>[F, G]): <~>[G, F]

    Natural isomorphism is commutative

  27. implicit def flipIso[A, B](implicit i: <=>[A, B]): <=>[B, A]

    Set isomorphism is commutative

  28. final def getClass(): Class[_]

    Definition Classes
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  29. def hashCode(): Int

    Definition Classes
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  30. final def isInstanceOf[T0]: Boolean

    Definition Classes
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  31. implicit def monoidCategory[M](implicit arg0: Monoid[M]): MonoidCategory[M]

  32. final def ne(arg0: AnyRef): Boolean

    Definition Classes
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  33. implicit def newTypeIso[A, B <: NewType[A]](implicit c: (A) ⇒ B): <=>[A, B]

    Every NewType is isomorphic to its underlying type.

    Every NewType is isomorphic to its underlying type. If its constructor is made implicit, we get an implicit isomorphism.

  34. final def notify(): Unit

    Definition Classes
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  35. final def notifyAll(): Unit

    Definition Classes
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  36. implicit def opContravariant[R]: Contravariant[[α]<=[R, α]]

  37. implicit def productCategory[UX <: Hom, UY <: Hom](implicit x: GeneralizedCategory { type U = UX }, y: GeneralizedCategory { type U = UY }): ProductCategory[UX, UY]

  38. def reflectIso[A1[_, _], A2[_, _], F[_], A, B](implicit c1: Category[A1], c2: Category[A2], f: GeneralizedFunctor[A2, A1, F]): (<~~>[[A, B]A1[F[A], F[B]], A2]) ⇒ (Iso[A1, F[A], F[B]]) ⇒ Iso[A2, A, B]

    Fully faithful functors reflect isomorphisms

  39. def stateAdjunction[S]: Adjunction[[S](S, S), [S](S) ⇒ S]

    The adjunction induced by curry and uncurry being isomorphic

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

    Definition Classes
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  41. def toString(): String

    Definition Classes
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  42. final def wait(): Unit

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    @throws()

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

    Definition Classes
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    @throws()

  44. final def wait(arg0: Long): Unit

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    @throws()

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