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 Source #

Constructors

Unit :: Unit () ()

Instances

Instances details

Category Unit Source #	`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 Source # tgt :: forall (a :: k) (b :: k). Unit a b -> Obj Unit b Source # (.) :: forall (b :: k) (c :: k) (a :: k). Unit b c -> Unit a b -> Unit a c Source #
CartesianClosed Unit Source #
Instance details Defined in Data.Category.CartesianClosed Associated Types type Exponential Unit y z :: Kind k Source # Methods apply :: forall (y :: k) (z :: k). Obj Unit y -> Obj Unit z -> Unit (BinaryProduct Unit (Exponential Unit y z) y) z Source # tuple :: forall (y :: k) (z :: k). Obj Unit y -> Obj Unit z -> Unit z (Exponential Unit y (BinaryProduct Unit z y)) Source # (^^^) :: forall (z1 :: k) (z2 :: k) (y2 :: k) (y1 :: k). Unit z1 z2 -> Unit y2 y1 -> Unit (Exponential Unit y1 z1) (Exponential Unit y2 z2) Source #
HasBinaryCoproducts Unit Source #	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 Source # Methods inj1 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit x (BinaryCoproduct Unit x y) Source # inj2 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit y (BinaryCoproduct Unit x y) Source # (\|\|\|) :: forall (x :: k) (a :: k) (y :: k). Unit x a -> Unit y a -> Unit (BinaryCoproduct Unit x y) a Source # (+++) :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). Unit a1 b1 -> Unit a2 b2 -> Unit (BinaryCoproduct Unit a1 a2) (BinaryCoproduct Unit b1 b2) Source #
HasBinaryProducts Unit Source #	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 Source # Methods proj1 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit (BinaryProduct Unit x y) x Source # proj2 :: forall (x :: k) (y :: k). Obj Unit x -> Obj Unit y -> Unit (BinaryProduct Unit x y) y Source # (&&&) :: forall (a :: k) (x :: k) (y :: k). Unit a x -> Unit a y -> Unit a (BinaryProduct Unit x y) Source # (***) :: forall (a1 :: k) (b1 :: k) (a2 :: k) (b2 :: k). Unit a1 b1 -> Unit a2 b2 -> Unit (BinaryProduct Unit a1 a2) (BinaryProduct Unit b1 b2) Source #
Category k => HasColimits Unit k Source #	The colimit of a single object is that object.
Instance details Defined in Data.Category.Limit Associated Types type ColimitFam Unit k f Source # Methods colimit :: Obj (Nat Unit k) f -> Cocone Unit k f (ColimitFam Unit k f) Source # colimitFactorizer :: Cocone Unit k f n -> k (ColimitFam Unit k f) n Source #
HasInitialObject Unit Source #	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 Source # Methods initialObject :: Obj Unit (InitialObject Unit) Source # initialize :: forall (a :: k). Obj Unit a -> Unit (InitialObject Unit) a Source #
Category k => HasLimits Unit k Source #	The limit of a single object is that object.
Instance details Defined in Data.Category.Limit Associated Types type LimitFam Unit k f Source # Methods limit :: Obj (Nat Unit k) f -> Cone Unit k f (LimitFam Unit k f) Source # limitFactorizer :: Cone Unit k f n -> k n (LimitFam Unit k f) Source #
HasTerminalObject Unit Source #	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 Source # Methods terminalObject :: Obj Unit (TerminalObject Unit) Source # terminate :: forall (a :: k). Obj Unit a -> Unit a (TerminalObject Unit) Source #
HasColimits j k => HasLeftKan (Const j Unit ()) k Source #	The left Kan extension of `f` along a functor to the unit category is the colimit of `f`.
Instance details Defined in Data.Category.KanExtension Associated Types type LanFam (Const j Unit ()) k f Source # Methods lan :: Const j Unit () -> Obj (Nat (Dom (Const j Unit ())) k) f -> Nat (Dom (Const j Unit ())) k f (LanFam (Const j Unit ()) k f :.: Const j Unit ()) Source # lanFactorizer :: Nat (Dom (Const j Unit ())) k f (h :.: Const j Unit ()) -> Nat (Cod (Const j Unit ())) k (LanFam (Const j Unit ()) k f) h Source #
HasLimits j k => HasRightKan (Const j Unit ()) k Source #	The right Kan extension of `f` along a functor to the unit category is the limit of `f`.
Instance details Defined in Data.Category.KanExtension Associated Types type RanFam (Const j Unit ()) k f Source # Methods ran :: Const j Unit () -> Obj (Nat (Dom (Const j Unit ())) k) f -> Nat (Dom (Const j Unit ())) k (RanFam (Const j Unit ()) k f :.: Const j Unit ()) f Source # ranFactorizer :: Nat (Dom (Const j Unit ())) k (h :.: Const j Unit ()) f -> Nat (Cod (Const j Unit ())) k h (RanFam (Const j Unit ()) k f) Source #
type InitialObject Unit Source #
Instance details Defined in Data.Category.Limit type InitialObject Unit = ()
type TerminalObject Unit Source #
Instance details Defined in Data.Category.Limit type TerminalObject Unit = ()
type ColimitFam Unit k f Source #
Instance details Defined in Data.Category.Limit type ColimitFam Unit k f = f :% ()
type LimitFam Unit k f Source #
Instance details Defined in Data.Category.Limit type LimitFam Unit k f = f :% ()
type Exponential Unit () () Source #
Instance details Defined in Data.Category.CartesianClosed type Exponential Unit () () = ()
type BinaryCoproduct Unit () () Source #
Instance details Defined in Data.Category.Limit type BinaryCoproduct Unit () () = ()
type BinaryProduct Unit () () Source #
Instance details Defined in Data.Category.Limit type BinaryProduct Unit () () = ()
type LanFam (Const j Unit ()) k f Source #
Instance details Defined in Data.Category.KanExtension type LanFam (Const j Unit ()) k f = Const Unit k (ColimitFam j k f)
type RanFam (Const j Unit ()) k f Source #
Instance details Defined in Data.Category.KanExtension type RanFam (Const j Unit ()) k f = Const Unit k (LimitFam j k f)