License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Category.Product

Description

Documentation

data (:**:) :: (Type -> Type -> Type) -> (Type -> Type -> Type) -> Type -> Type -> Type where Source #

Constructors

(:**:) :: c1 a1 b1 -> c2 a2 b2 -> (:**:) c1 c2 (a1, a2) (b1, b2)

Instances

Instances details

(Category c1, Category c2) => Category (c1 :**: c2 :: Type -> Type -> Type) Source #	The product category of categories `c1` and `c2`.
Instance details Defined in Data.Category.Product Methods src :: forall (a :: k) (b :: k). (c1 :: c2) a b -> Obj (c1 :: c2) a Source # tgt :: forall (a :: k) (b :: k). (c1 :: c2) a b -> Obj (c1 :: c2) b Source # (.) :: forall (b :: k) (c :: k) (a :: k). (c1 :: c2) b c -> (c1 :: c2) a b -> (c1 :**: c2) a c Source #
(HasBinaryCoproducts c1, HasBinaryCoproducts c2) => HasBinaryCoproducts (c1 :**: c2 :: Type -> Type -> Type) Source #	The binary coproduct of the product of 2 categories is the product of their binary coproducts.
Instance details Defined in Data.Category.Limit Associated Types type BinaryCoproduct (c1 :: c2) x y :: Kind k Source # Methods inj1 :: forall (x :: k) (y :: k). Obj (c1 :: c2) x -> Obj (c1 :: c2) y -> (c1 :: c2) x (BinaryCoproduct (c1 :: c2) x y) Source # inj2 :: forall (x :: k) (y :: k). Obj (c1 :: c2) x -> Obj (c1 :: c2) y -> (c1 :: c2) y (BinaryCoproduct (c1 :: c2) x y) Source # (\|\|\|) :: forall (x :: k) (a :: k) (y :: k). (c1 :: c2) x a -> (c1 :: c2) y a -> (c1 :: c2) (BinaryCoproduct (c1 :: c2) x y) a Source # (+++) :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). (c1 :: c2) a1 b1 -> (c1 :: c2) a2 b2 -> (c1 :: c2) (BinaryCoproduct (c1 :: c2) a1 a2) (BinaryCoproduct (c1 :: c2) b1 b2) Source #
(HasBinaryProducts c1, HasBinaryProducts c2) => HasBinaryProducts (c1 :**: c2 :: Type -> Type -> Type) Source #	The binary product of the product of 2 categories is the product of their binary products.
Instance details Defined in Data.Category.Limit Associated Types type BinaryProduct (c1 :: c2) x y :: Kind k Source # Methods proj1 :: forall (x :: k) (y :: k). Obj (c1 :: c2) x -> Obj (c1 :: c2) y -> (c1 :: c2) (BinaryProduct (c1 :: c2) x y) x Source # proj2 :: forall (x :: k) (y :: k). Obj (c1 :: c2) x -> Obj (c1 :: c2) y -> (c1 :: c2) (BinaryProduct (c1 :: c2) x y) y Source # (&&&) :: forall (a :: k) (x :: k) (y :: k). (c1 :: c2) a x -> (c1 :: c2) a y -> (c1 :: c2) a (BinaryProduct (c1 :: c2) x y) Source # () :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). (c1 :: c2) a1 b1 -> (c1 :: c2) a2 b2 -> (c1 :: c2) (BinaryProduct (c1 :: c2) a1 a2) (BinaryProduct (c1 :*: c2) b1 b2) Source #
(HasInitialObject c1, HasInitialObject c2) => HasInitialObject (c1 :**: c2 :: Type -> Type -> Type) Source #	The initial object of the product of 2 categories is the product of their initial objects.
Instance details Defined in Data.Category.Limit Associated Types type InitialObject (c1 :: c2) :: Kind k Source # Methods initialObject :: Obj (c1 :: c2) (InitialObject (c1 :: c2)) Source # initialize :: forall (a :: k). Obj (c1 :: c2) a -> (c1 :: c2) (InitialObject (c1 :: c2)) a Source #
(HasTerminalObject c1, HasTerminalObject c2) => HasTerminalObject (c1 :**: c2 :: Type -> Type -> Type) Source #	The terminal object of the product of 2 categories is the product of their terminal objects.
Instance details Defined in Data.Category.Limit Associated Types type TerminalObject (c1 :: c2) :: Kind k Source # Methods terminalObject :: Obj (c1 :: c2) (TerminalObject (c1 :: c2)) Source # terminate :: forall (a :: k). Obj (c1 :: c2) a -> (c1 :: c2) a (TerminalObject (c1 :: c2)) Source #
type InitialObject (c1 :**: c2 :: Type -> Type -> Type) Source #
Instance details Defined in Data.Category.Limit type InitialObject (c1 :**: c2 :: Type -> Type -> Type) = (InitialObject c1, InitialObject c2)
type TerminalObject (c1 :**: c2 :: Type -> Type -> Type) Source #
Instance details Defined in Data.Category.Limit type TerminalObject (c1 :**: c2 :: Type -> Type -> Type) = (TerminalObject c1, TerminalObject c2)
type BinaryCoproduct (c1 :: c2 :: Type -> Type -> Type) ((x1, x2) :: Kind (c1 :: c2)) ((y1, y2) :: Kind (c1 :**: c2)) Source #
Instance details Defined in Data.Category.Limit type BinaryCoproduct (c1 :: c2 :: Type -> Type -> Type) ((x1, x2) :: Kind (c1 :: c2)) ((y1, y2) :: Kind (c1 :**: c2)) = (BinaryCoproduct c1 x1 y1, BinaryCoproduct c2 x2 y2)
type BinaryProduct (c1 :: c2 :: Type -> Type -> Type) ((x1, x2) :: Kind (c1 :: c2)) ((y1, y2) :: Kind (c1 :**: c2)) Source #
Instance details Defined in Data.Category.Limit type BinaryProduct (c1 :: c2 :: Type -> Type -> Type) ((x1, x2) :: Kind (c1 :: c2)) ((y1, y2) :: Kind (c1 :**: c2)) = (BinaryProduct c1 x1 y1, BinaryProduct c2 x2 y2)