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

Minimal complete definition

o

Methods

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

Instances

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

Defined in Data.Semigroupoid

Methods

o :: (j :~: k0) -> (i :~: j) -> i :~: k0

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

Defined in Data.Semigroupoid

Methods

o :: Coercion j k0 -> Coercion i j -> Coercion i k0

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

Defined in Data.Semigroupoid

Methods

o :: (j :~~: k0) -> (i :~~: j) -> i :~~: k0

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

Defined in Data.Isomorphism

Methods

o :: Iso k2 j k -> Iso k2 i j -> Iso k2 i k

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

Defined in Data.Semigroupoid

Methods

o :: WrappedCategory k2 j k -> WrappedCategory k2 i j -> WrappedCategory k2 i k

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

Defined in Data.Semigroupoid

Methods

o :: Semi m j k0 -> Semi m i j -> Semi m i k0

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

Defined in Data.Semigroupoid.Dual

Methods

o :: Dual k2 j k -> Dual k2 i j -> Dual k2 i k

Semigroupoid (,)

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

Defined in Data.Semigroupoid

Methods

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

Semigroupoid Op

Defined in Data.Semigroupoid

Methods

o :: Op j k -> Op i j -> Op i k

Bind m => Semigroupoid (Kleisli m :: * -> * -> *)

Defined in Data.Semigroupoid

Methods

o :: Kleisli m j k -> Kleisli m i j -> Kleisli m i k

Semigroupoid (Const :: * -> * -> *)

Defined in Data.Semigroupoid

Methods

o :: Const j k -> Const i j -> Const i k

Semigroupoid (Tagged :: * -> * -> *)

Defined in Data.Semigroupoid

Methods

o :: Tagged j k -> Tagged i j -> Tagged i k

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

Defined in Data.Semigroupoid.Static

Methods

o :: Static f j k -> Static f i j -> Static f i k

Semigroupoid ((->) :: * -> * -> *)

Defined in Data.Semigroupoid

Methods

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

Extend w => Semigroupoid (Cokleisli w :: * -> * -> *)

Defined in Data.Semigroupoid

Methods

o :: Cokleisli w j k -> Cokleisli w i j -> Cokleisli w i k

newtype WrappedCategory k a b

Constructors

WrapCategory

Fields

• unwrapCategory :: k a b

Instances

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

Defined in Data.Semigroupoid

Methods

id :: WrappedCategory k2 a a

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

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

Defined in Data.Semigroupoid

Methods

o :: 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 -> *)

Defined in Data.Semigroupoid

Methods

id :: Semi m a a

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

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

Defined in Data.Semigroupoid

Methods

o :: Semi m j k0 -> Semi m i j -> Semi m i k0