Data.Semigroupoid

A semigroupoid satisfies all of the requirements to be a Category except for the existence of identity arrows.

Documentation

class Semigroupoid c where

Category sans id

Methods

o :: c j k -> c i j -> c i k

Instances

Semigroupoid Op

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). Op j k -> Op i j -> Op i k

Semigroupoid (,)

http://en.wikipedia.org/wiki/Band_(mathematics)#Rectangular_bands

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). (j, k) -> (i, j) -> (i, k)

Bind m => Semigroupoid (Kleisli m :: Type -> Type -> TYPE LiftedRep)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). Kleisli m j k -> Kleisli m i j -> Kleisli m i k

Semigroupoid (Const :: Type -> Type -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). Const j k -> Const i j -> Const i k

Semigroupoid s => Semigroupoid (Categorical s :: Type -> Type -> Type)

Since: 5.3.6

Defined in Data.Semigroupoid.Categorical

Methods

o :: forall (j :: k) (k :: k) (i :: k). Categorical s j k -> Categorical s i j -> Categorical s i k

Apply f => Semigroupoid (Static f :: Type -> Type -> Type)

Defined in Data.Semigroupoid.Static

Methods

o :: forall (j :: k) (k :: k) (i :: k). Static f j k -> Static f i j -> Static f i k

Semigroupoid (Tagged :: Type -> Type -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). Tagged j k -> Tagged i j -> Tagged i k

Semigroupoid (Coercion :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k0) (k1 :: k0) (i :: k0). Coercion j k1 -> Coercion i j -> Coercion i k1

Semigroupoid ((:~:) :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k0) (k1 :: k0) (i :: k0). (j :~: k1) -> (i :~: j) -> i :~: k1

Extend w => Semigroupoid (Cokleisli w :: Type -> Type -> TYPE LiftedRep)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). Cokleisli w j k -> Cokleisli w i j -> Cokleisli w i k

Semigroupoid (->)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). (j -> k) -> (i -> j) -> i -> k

Semigroupoid ((:~~:) :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k0) (k1 :: k0) (i :: k0). (j :~~: k1) -> (i :~~: j) -> i :~~: k1

Semigroupoid k2 => Semigroupoid (Iso k2 :: k1 -> k1 -> Type)

Defined in Data.Isomorphism

Methods

o :: forall (j :: k) (k :: k) (i :: k). Iso k2 j k -> Iso k2 i j -> Iso k2 i k

Semigroup m => Semigroupoid (Semi m :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k0) (k1 :: k0) (i :: k0). Semi m j k1 -> Semi m i j -> Semi m i k1

Category k2 => Semigroupoid (WrappedCategory k2 :: k1 -> k1 -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). WrappedCategory k2 j k -> WrappedCategory k2 i j -> WrappedCategory k2 i k

Semigroupoid k2 => Semigroupoid (Dual k2 :: k1 -> k1 -> Type)

Defined in Data.Semigroupoid.Dual

Methods

o :: forall (j :: k) (k :: k) (i :: k). Dual k2 j k -> Dual k2 i j -> Dual k2 i k

newtype WrappedCategory k a b

Constructors

WrapCategory

Fields

• unwrapCategory :: k a b

Instances

Category k2 => Category (WrappedCategory k2 :: k1 -> k1 -> Type)

Defined in Data.Semigroupoid

Methods

id :: forall (a :: k). WrappedCategory k2 a a

(.) :: forall (b :: k) (c :: k) (a :: k). WrappedCategory k2 b c -> WrappedCategory k2 a b -> WrappedCategory k2 a c

Category k2 => Semigroupoid (WrappedCategory k2 :: k1 -> k1 -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k) (k :: k) (i :: k). WrappedCategory k2 j k -> WrappedCategory k2 i j -> WrappedCategory k2 i k

newtype Semi m a b

Constructors

Semi

Fields

• getSemi :: m

Instances

Monoid m => Category (Semi m :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

id :: forall (a :: k0). Semi m a a

(.) :: forall (b :: k0) (c :: k0) (a :: k0). Semi m b c -> Semi m a b -> Semi m a c

Semigroup m => Semigroupoid (Semi m :: k -> k -> Type)

Defined in Data.Semigroupoid

Methods

o :: forall (j :: k0) (k1 :: k0) (i :: k0). Semi m j k1 -> Semi m i j -> Semi m i k1