Safe Haskell	None
Language	GHC2024

Proarrow.Profunctor.Yoneda

Contents

Orphan instances

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 Github #

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

Instances details

(CategoryOf j, CategoryOf k) => Profunctor (Yoneda p :: k -> j -> Type) Source Github #
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 Github # lmap :: forall (c :: k) (a :: k) (b :: j). (c ~> a) -> Yoneda p a b -> Yoneda p c b Source Github # rmap :: forall (b :: j) (d :: j) (a :: k). (b ~> d) -> Yoneda p a b -> Yoneda p a d Source Github # (\\) :: forall (a :: k) (b :: j) r. ((Ob a, Ob b) => r) -> Yoneda p a b -> r Source Github #
Functor (Yoneda :: (j +-> k) -> k -> j -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods map :: forall (a :: j +-> k) (b :: j +-> k). (a ~> b) -> Yoneda a ~> Yoneda b Source Github #
Promonad (Costar (Yoneda :: (j +-> k) -> k -> j -> Type) :: (j +-> k) -> (k -> j -> Type) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods id :: forall (a :: j +-> k). Ob a => Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: j +-> k) (c :: j +-> k) (a :: j +-> k). Costar (Yoneda :: (j +-> k) -> k -> j -> Type) b c -> Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a b -> Costar (Yoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #
Promonad (Star (Yoneda :: (j +-> k) -> k -> j -> Type) :: (k -> j -> Type) -> (j +-> k) -> Type) Source Github #
Instance details Defined in Proarrow.Profunctor.Yoneda Methods id :: forall (a :: k -> j -> Type). Ob a => Star (Yoneda :: (j +-> k) -> k -> j -> Type) a a Source Github # (.) :: forall (b :: k -> j -> Type) (c :: k -> j -> Type) (a :: k -> j -> Type). Star (Yoneda :: (j +-> k) -> k -> j -> Type) b c -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a b -> Star (Yoneda :: (j +-> k) -> k -> j -> Type) a c Source Github #

yoneda :: forall j k (p :: j +-> k). (CategoryOf j, CategoryOf k) => Yoneda p :~> p Source Github #

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

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

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

Instances details

(CategoryOf j, CategoryOf k) => Profunctor (Yo a ('OP b) :: k -> j -> Type) Source Github #
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 Github # lmap :: forall (c :: k) (a0 :: k) (b0 :: j). (c ~> a0) -> Yo a ('OP b) a0 b0 -> Yo a ('OP b) c b0 Source Github # rmap :: forall (b0 :: j) (d :: j) (a0 :: k). (b0 ~> d) -> Yo a ('OP b) a0 b0 -> Yo a ('OP b) a0 d Source Github # (\\) :: forall (a0 :: k) (b0 :: j) r. ((Ob a0, Ob b0) => r) -> Yo a ('OP b) a0 b0 -> r Source Github #
(CategoryOf j, CategoryOf k) => Functor (Yo :: k -> OPPOSITE j -> k -> j -> Type) Source Github #
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 Github #
(CategoryOf j, CategoryOf k) => Functor (Yo a :: OPPOSITE j -> k -> j -> Type) Source Github #
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 Github #

Orphan instances

HasCofree (Profunctor :: (j +-> k) -> Constraint) Source Github #
Instance details Methods lower :: forall (a :: j +-> k). Ob a => Cofree (Profunctor :: (j +-> k) -> Constraint) a ~> a Source Github # unfoldMap :: forall (a :: j +-> k) (b :: j +-> k). Profunctor a => (a ~> b) -> a ~> Cofree (Profunctor :: (j +-> k) -> Constraint) b Source Github #