Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.Zero

Documentation

data VOID Source Comments #

Instances

Instances details

CategoryOf VOID Source Comments #

The category with no objects, the initial category.

Instance details

Defined in Proarrow.Category.Instance.Zero

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Zero type (~>) = Zero
type Ob (a :: VOID)
Instance details Defined in Proarrow.Category.Instance.Zero type Ob (a :: VOID) = Bottom

DaggerProfunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dagger :: forall (a :: VOID) (b :: VOID). Zero a b -> Zero b a Source Comments #

Promonad Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

id :: forall (a :: VOID). Ob a => Zero a a Source Comments #

(.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Comments #

ThinProfunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Associated Types

type HasArrow Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Instance.Zero type HasArrow Zero (a :: VOID) (b :: VOID) = ()

Methods

arr :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b, HasArrow Zero a b) => Zero a b Source Comments #

withArr :: forall (a :: VOID) (b :: VOID) r. Zero a b -> (HasArrow Zero a b => r) -> r Source Comments #

Profunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dimap :: forall (c :: VOID) (a :: VOID) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Zero a b -> Zero c d Source Comments #

(\\) :: forall (a :: VOID) (b :: VOID) r. ((Ob a, Ob b) => r) -> Zero a b -> r Source Comments #

CategoryOf k => FunctorForRep (Initiate :: VOID +-> k) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Cat

Methods

fmap :: forall (a :: VOID) (b :: VOID). (a ~> b) -> ((Initiate :: VOID +-> k) @ a) ~> ((Initiate :: VOID +-> k) @ b) Source Comments #

HasInitialObject k => HasColimits (Unweighted :: VOID -> () -> Type) k Source Comments #

Instance details

Defined in Proarrow.Category.Colimit

Methods

colimit :: forall (d :: k +-> VOID). Corepresentable d => ((Unweighted :: VOID -> () -> Type) :.: Colimit (Unweighted :: VOID -> () -> Type) d) :~> d Source Comments #

colimitUniv :: forall (d :: k +-> VOID) (p :: k +-> ()). (Corepresentable d, Profunctor p) => (((Unweighted :: VOID -> () -> Type) :.: p) :~> d) -> p :~> Colimit (Unweighted :: VOID -> () -> Type) d Source Comments #

HasTerminalObject k => HasLimits (Unweighted :: () -> VOID -> Type) k Source Comments #

Instance details

Defined in Proarrow.Category.Limit

Methods

limit :: forall (d :: VOID +-> k). Representable d => (Limit (Unweighted :: () -> VOID -> Type) d :.: (Unweighted :: () -> VOID -> Type)) :~> d Source Comments #

limitUniv :: forall (d :: VOID +-> k) (p :: () +-> k). (Representable d, Profunctor p) => ((p :.: (Unweighted :: () -> VOID -> Type)) :~> d) -> p :~> Limit (Unweighted :: () -> VOID -> Type) d Source Comments #

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

type (~>) = Zero

type Ob (a :: VOID) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

type Ob (a :: VOID) = Bottom

type HasArrow Zero (a :: VOID) (b :: VOID) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

type HasArrow Zero (a :: VOID) (b :: VOID) = ()

type Colimit (Unweighted :: VOID -> () -> Type) (d :: k +-> VOID) Source Comments #

Instance details

Defined in Proarrow.Category.Colimit

type Colimit (Unweighted :: VOID -> () -> Type) (d :: k +-> VOID) = InitialLimit d

type Limit (Unweighted :: () -> VOID -> Type) (d :: VOID +-> k) Source Comments #

Instance details

Defined in Proarrow.Category.Limit

type Limit (Unweighted :: () -> VOID -> Type) (d :: VOID +-> k) = Rep (TerminalLimit d)

type (Initiate :: VOID +-> k) @ (a :: VOID) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Cat

type (Initiate :: VOID +-> k) @ (a :: VOID) = Any :: k

data Zero (a :: VOID) (b :: VOID) Source Comments #

Instances

Instances details

DaggerProfunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dagger :: forall (a :: VOID) (b :: VOID). Zero a b -> Zero b a Source Comments #

Promonad Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

id :: forall (a :: VOID). Ob a => Zero a a Source Comments #

(.) :: forall (b :: VOID) (c :: VOID) (a :: VOID). Zero b c -> Zero a b -> Zero a c Source Comments #

ThinProfunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Associated Types

type HasArrow Zero (a :: VOID) (b :: VOID)
Instance details Defined in Proarrow.Category.Instance.Zero type HasArrow Zero (a :: VOID) (b :: VOID) = ()

Methods

arr :: forall (a :: VOID) (b :: VOID). (Ob a, Ob b, HasArrow Zero a b) => Zero a b Source Comments #

withArr :: forall (a :: VOID) (b :: VOID) r. Zero a b -> (HasArrow Zero a b => r) -> r Source Comments #

Profunctor Zero Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Zero

Methods

dimap :: forall (c :: VOID) (a :: VOID) (b :: VOID) (d :: VOID). (c ~> a) -> (b ~> d) -> Zero a b -> Zero c d Source Comments #

(\\) :: forall (a :: VOID) (b :: VOID) r. ((Ob a, Ob b) => r) -> Zero a b -> r Source Comments #