Safe Haskell	None
Language	Haskell2010

Proarrow.Profunctor.Yoneda

Contents

Synopsis

data Yoneda (p :: j +-> k) (a :: k) (b :: j) where
- Yoneda :: forall {k} {j} (a :: k) (b :: j) (p :: j +-> k). (Ob a, Ob b) => {..} -> Yoneda p a b
yoneda :: forall j k (p :: j +-> k). (CategoryOf j, CategoryOf k) => Yoneda p :~> p
mkYoneda :: forall {j} {k} (p :: j +-> k). Profunctor p => p :~> Yoneda p
data Yo (a :: k) (b :: OPPOSITE j) (c :: k) (d :: j) where
- Yo :: forall {k} {j} (c :: k) (a :: k) (b1 :: j) (d :: j). (c ~> a) -> (b1 ~> d) -> Yo a ('OP b1) c d

Documentation

data Yoneda (p :: j +-> k) (a :: k) (b :: j) where Source Comments #

Constructors

Yoneda
Fields :: forall {k} {j} (a :: k) (b :: j) (p :: j +-> k). (Ob a, Ob b) => { unYoneda :: Yo a ('OP b) :~> p } -> Yoneda p a b

Instances details

(CategoryOf j, CategoryOf k) => Profunctor (Yoneda p :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: k) (a :: k) (b :: j) (d :: j). (c ~> a) -> (b ~> d) -> Yoneda p a b -> Yoneda p c d Source Comments # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Yoneda p a b -> r Source Comments #
Functor (Yoneda :: (j +-> k) -> k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods map :: forall (a :: j +-> k) (b :: j +-> k). (a ~> b) -> Yoneda a ~> Yoneda b Source Comments #

mkYoneda :: forall {j} {k} (p :: j +-> k). Profunctor p => p :~> Yoneda p Source Comments #

data Yo (a :: k) (b :: OPPOSITE j) (c :: k) (d :: j) where Source Comments #

Yoneda embedding

Constructors

Yo :: forall {k} {j} (c :: k) (a :: k) (b1 :: j) (d :: j). (c ~> a) -> (b1 ~> d) -> Yo a ('OP b1) c d

Instances details

(CategoryOf j, CategoryOf k) => Profunctor (Yo a ('OP b) :: k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods dimap :: forall (c :: k) (a0 :: k) (b0 :: j) (d :: j). (c ~> a0) -> (b0 ~> d) -> Yo a ('OP b) a0 b0 -> Yo a ('OP b) c d Source Comments # (\\) :: forall (a0 :: k) (b0 :: j) r. ((Ob a0, Ob b0) => r) -> Yo a ('OP b) a0 b0 -> r Source Comments #
(CategoryOf j, CategoryOf k) => Functor (Yo :: k -> OPPOSITE j -> k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods map :: forall (a :: k) (b :: k). (a ~> b) -> (Yo a :: OPPOSITE j -> k -> j -> Type) ~> (Yo b :: OPPOSITE j -> k -> j -> Type) Source Comments #
(CategoryOf j, CategoryOf k) => Functor (Yo a :: OPPOSITE j -> k -> j -> Type) Source Comments #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods map :: forall (a0 :: OPPOSITE j) (b :: OPPOSITE j). (a0 ~> b) -> Yo a a0 ~> Yo a b Source Comments #

Orphan instances

Instance details

Associated Types

type Cofree (Profunctor :: (j +-> k) -> Constraint)
Instance details Defined in Proarrow.Profunctor.Yoneda type Cofree (Profunctor :: (j +-> k) -> Constraint) = Star (Yoneda :: (j +-> k) -> k -> j -> Type)

Methods

lower' :: forall (a :: j +-> k) (b :: j +-> k). Cofree (Profunctor :: (j +-> k) -> Constraint) a b -> a ~> b Source Comments #

section' :: forall (a :: j +-> k) (b :: j +-> k). Profunctor a => (a ~> b) -> Cofree (Profunctor :: (j +-> k) -> Constraint) a b Source Comments #