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

Data.Category.Unit

Description

Documentation

data Unit a b where #

Constructors

Unit :: Unit () ()

Instances

Instances details

Category k => HasColimits Unit k #	The colimit of a single object is that object.
Instance details Defined in Data.Category.Limit Methods colimit :: Obj (Nat Unit k) f -> Cocone Unit k f (ColimitFam Unit k f) # colimitFactorizer :: Cocone Unit k f n -> k (ColimitFam Unit k f) n #
Category k => HasLimits Unit k #	The limit of a single object is that object.
Instance details Defined in Data.Category.Limit Methods limit :: Obj (Nat Unit k) f -> Cone Unit k f (LimitFam Unit k f) # limitFactorizer :: Cone Unit k f n -> k n (LimitFam Unit k f) #
Category Unit #	`Unit` is the category with one object.
Instance details Defined in Data.Category.Unit Methods src :: forall (a :: k) (b :: k). Unit a b -> Obj Unit a # tgt :: forall (a :: k) (b :: k). Unit a b -> Obj Unit b # (.) :: forall (b :: k) (c :: k) (a :: k). Unit b c -> Unit a b -> Unit a c #
HasBinaryCoproducts Unit #	In the category of one object that object is its own coproduct.
Instance details Defined in Data.Category.Limit Associated Types type BinaryCoproduct Unit x y :: Kind k # Methods inj1 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit x (BinaryCoproduct Unit x y) # inj2 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit y (BinaryCoproduct Unit x y) # (\|\|\|) :: forall (x :: k) (a :: k) (y :: k). Unit x a -> Unit y a -> Unit (BinaryCoproduct Unit x y) a # (+++) :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). Unit a1 b1 -> Unit a2 b2 -> Unit (BinaryCoproduct Unit a1 a2) (BinaryCoproduct Unit b1 b2) #
HasBinaryProducts Unit #	In the category of one object that object is its own product.
Instance details Defined in Data.Category.Limit Associated Types type BinaryProduct Unit x y :: Kind k # Methods proj1 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit (BinaryProduct Unit x y) x # proj2 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit (BinaryProduct Unit x y) y # (&&&) :: forall (a :: k) (x :: k) (y :: k). Unit a x -> Unit a y -> Unit a (BinaryProduct Unit x y) # (***) :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). Unit a1 b1 -> Unit a2 b2 -> Unit (BinaryProduct Unit a1 a2) (BinaryProduct Unit b1 b2) #
HasInitialObject Unit #	The category of one object has that object as initial object.
Instance details Defined in Data.Category.Limit Associated Types type InitialObject Unit :: Kind k # Methods initialObject :: Obj Unit (InitialObject Unit) # initialize :: forall (a :: k). Obj Unit a -> Unit (InitialObject Unit) a #
HasTerminalObject Unit #	The category of one object has that object as terminal object.
Instance details Defined in Data.Category.Limit Associated Types type TerminalObject Unit :: Kind k # Methods terminalObject :: Obj Unit (TerminalObject Unit) # terminate :: forall (a :: k). Obj Unit a -> Unit a (TerminalObject Unit) #
CartesianClosed Unit #
Instance details Defined in Data.Category.CartesianClosed Associated Types type Exponential Unit y z :: Kind k # Methods apply :: forall (y :: k) (z :: k). Obj Unit y -> Obj Unit z -> Unit (BinaryProduct Unit (Exponential Unit y z) y) z # tuple :: forall (y :: k) (z :: k). Obj Unit y -> Obj Unit z -> Unit z (Exponential Unit y (BinaryProduct Unit z y)) # (^^^) :: forall (z1 :: k) (z2 :: k) (y2 :: k) (y1 :: k). Unit z1 z2 -> Unit y2 y1 -> Unit (Exponential Unit y1 z1) (Exponential Unit y2 z2) #
type ColimitFam Unit k f #
Instance details Defined in Data.Category.Limit type ColimitFam Unit k f = f :% ()
type LimitFam Unit k f #
Instance details Defined in Data.Category.Limit type LimitFam Unit k f = f :% ()
type InitialObject Unit #
Instance details Defined in Data.Category.Limit type InitialObject Unit = ()
type TerminalObject Unit #
Instance details Defined in Data.Category.Limit type TerminalObject Unit = ()
type BinaryCoproduct Unit () () #
Instance details Defined in Data.Category.Limit type BinaryCoproduct Unit () () = ()
type BinaryProduct Unit () () #
Instance details Defined in Data.Category.Limit type BinaryProduct Unit () () = ()
type Exponential Unit () () #
Instance details Defined in Data.Category.CartesianClosed type Exponential Unit () () = ()