License	BSD-style (see the file LICENSE)
Maintainer	sjoerd@w3future.com
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.Category.Boolean

Description

2, or the Boolean category. It contains 2 objects, one for true and one for false. It contains 3 arrows, 2 identity arrows and one from false to true.

Documentation

data Fls Source #

Instances

type BinaryCoproduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Tru Fls = Tru
type BinaryCoproduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Fls Tru = Tru
type BinaryCoproduct Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Fls Fls = Fls
type BinaryProduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Tru Fls = Fls
type BinaryProduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Fls Tru = Fls
type BinaryProduct Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Fls Fls = Fls
type Exponential Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Tru Fls = Fls
type Exponential Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Fls Tru = Tru
type Exponential Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Fls Fls = Tru
type (Arrow k a b) :% Fls Source #
Instance details Defined in Data.Category.Boolean type (Arrow k a b) :% Fls = a

data Tru Source #

Instances

type BinaryCoproduct Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Tru Tru = Tru
type BinaryCoproduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Tru Fls = Tru
type BinaryCoproduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Fls Tru = Tru
type BinaryProduct Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Tru Tru = Tru
type BinaryProduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Tru Fls = Fls
type BinaryProduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Fls Tru = Fls
type Exponential Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Tru Tru = Tru
type Exponential Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Tru Fls = Fls
type Exponential Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Fls Tru = Tru
type (Arrow k a b) :% Tru Source #
Instance details Defined in Data.Category.Boolean type (Arrow k a b) :% Tru = b

data Boolean a b where Source #

Constructors

Fls :: Boolean Fls Fls
F2T :: Boolean Fls Tru
Tru :: Boolean Tru Tru

Instances

Category Boolean Source #	`Boolean` is the category with true and false as objects, and an arrow from false to true.
Instance details Defined in Data.Category.Boolean Methods src :: Boolean a b -> Obj Boolean a Source # tgt :: Boolean a b -> Obj Boolean b Source # (.) :: Boolean b c -> Boolean a b -> Boolean a c Source #
HasBinaryCoproducts Boolean Source #	Disjunction is the binary coproduct in the Boolean category.
Instance details Defined in Data.Category.Boolean Associated Types type BinaryCoproduct Boolean x y :: Type Source # Methods inj1 :: Obj Boolean x -> Obj Boolean y -> Boolean x (BinaryCoproduct Boolean x y) Source # inj2 :: Obj Boolean x -> Obj Boolean y -> Boolean y (BinaryCoproduct Boolean x y) Source # (\|\|\|) :: Boolean x a -> Boolean y a -> Boolean (BinaryCoproduct Boolean x y) a Source # (+++) :: Boolean a1 b1 -> Boolean a2 b2 -> Boolean (BinaryCoproduct Boolean a1 a2) (BinaryCoproduct Boolean b1 b2) Source #
HasBinaryProducts Boolean Source #	Conjunction is the binary product in the Boolean category.
Instance details Defined in Data.Category.Boolean Associated Types type BinaryProduct Boolean x y :: Type Source # Methods proj1 :: Obj Boolean x -> Obj Boolean y -> Boolean (BinaryProduct Boolean x y) x Source # proj2 :: Obj Boolean x -> Obj Boolean y -> Boolean (BinaryProduct Boolean x y) y Source # (&&&) :: Boolean a x -> Boolean a y -> Boolean a (BinaryProduct Boolean x y) Source # (***) :: Boolean a1 b1 -> Boolean a2 b2 -> Boolean (BinaryProduct Boolean a1 a2) (BinaryProduct Boolean b1 b2) Source #
HasInitialObject Boolean Source #	False is the initial object in the Boolean category.
Instance details Defined in Data.Category.Boolean Associated Types type InitialObject Boolean :: Type Source # Methods initialObject :: Obj Boolean (InitialObject Boolean) Source # initialize :: Obj Boolean a -> Boolean (InitialObject Boolean) a Source #
HasTerminalObject Boolean Source #	True is the terminal object in the Boolean category.
Instance details Defined in Data.Category.Boolean Associated Types type TerminalObject Boolean :: Type Source # Methods terminalObject :: Obj Boolean (TerminalObject Boolean) Source # terminate :: Obj Boolean a -> Boolean a (TerminalObject Boolean) Source #
CartesianClosed Boolean Source #	Implication makes the Boolean category cartesian closed.
Instance details Defined in Data.Category.Boolean Associated Types type Exponential Boolean y z :: Type Source # Methods apply :: Obj Boolean y -> Obj Boolean z -> Boolean (BinaryProduct Boolean (Exponential Boolean y z) y) z Source # tuple :: Obj Boolean y -> Obj Boolean z -> Boolean z (Exponential Boolean y (BinaryProduct Boolean z y)) Source # (^^^) :: Boolean z1 z2 -> Boolean y2 y1 -> Boolean (Exponential Boolean y1 z1) (Exponential Boolean y2 z2) Source #
Category k => HasColimits Boolean k Source #	The colimit of a functor from the Boolean category is the target of the arrow it points to.
Instance details Defined in Data.Category.Boolean Methods colimit :: Obj (Nat Boolean k) f -> Cocone f (Colimit f) Source # colimitFactorizer :: Obj (Nat Boolean k) f -> Cocone f n -> k (Colimit f) n Source #
Category k => HasLimits Boolean k Source #	The limit of a functor from the Boolean category is the source of the arrow it points to.
Instance details Defined in Data.Category.Boolean Methods limit :: Obj (Nat Boolean k) f -> Cone f (Limit f) Source # limitFactorizer :: Obj (Nat Boolean k) f -> Cone f n -> k n (Limit f) Source #
type InitialObject Boolean Source #
Instance details Defined in Data.Category.Boolean type InitialObject Boolean = Fls
type TerminalObject Boolean Source #
Instance details Defined in Data.Category.Boolean type TerminalObject Boolean = Tru
type BinaryCoproduct Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Tru Tru = Tru
type BinaryCoproduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Tru Fls = Tru
type BinaryCoproduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Fls Tru = Tru
type BinaryCoproduct Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryCoproduct Boolean Fls Fls = Fls
type BinaryProduct Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Tru Tru = Tru
type BinaryProduct Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Tru Fls = Fls
type BinaryProduct Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Fls Tru = Fls
type BinaryProduct Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type BinaryProduct Boolean Fls Fls = Fls
type ColimitFam Boolean k f Source #
Instance details Defined in Data.Category.Boolean type ColimitFam Boolean k f = f :% Tru
type LimitFam Boolean k f Source #
Instance details Defined in Data.Category.Boolean type LimitFam Boolean k f = f :% Fls
type Exponential Boolean Tru Tru Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Tru Tru = Tru
type Exponential Boolean Tru Fls Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Tru Fls = Fls
type Exponential Boolean Fls Tru Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Fls Tru = Tru
type Exponential Boolean Fls Fls Source #
Instance details Defined in Data.Category.Boolean type Exponential Boolean Fls Fls = Tru

trueProductMonoid :: MonoidObject (ProductFunctor Boolean) Tru Source #

falseCoproductComonoid :: ComonoidObject (CoproductFunctor Boolean) Fls Source #

trueProductComonoid :: ComonoidObject (ProductFunctor Boolean) Tru Source #

falseCoproductMonoid :: MonoidObject (CoproductFunctor Boolean) Fls Source #

trueCoproductMonoid :: MonoidObject (CoproductFunctor Boolean) Tru Source #

falseProductComonoid :: ComonoidObject (ProductFunctor Boolean) Fls Source #

data Arrow k a b Source #

Constructors

Arrow (k a b)

Instances

Category k => Functor (Arrow k a b) Source #	Any functor from the Boolean category points to an arrow in its target category.
Instance details Defined in Data.Category.Boolean Associated Types type Dom (Arrow k a b) :: Type -> Type -> Type Source # type Cod (Arrow k a b) :: Type -> Type -> Type Source # type (Arrow k a b) :% a :: Type Source # Methods (%) :: Arrow k a b -> Dom (Arrow k a b) a0 b0 -> Cod (Arrow k a b) (Arrow k a b :% a0) (Arrow k a b :% b0) Source #
type Dom (Arrow k a b) Source #
Instance details Defined in Data.Category.Boolean type Dom (Arrow k a b) = Boolean
type Cod (Arrow k a b) Source #
Instance details Defined in Data.Category.Boolean type Cod (Arrow k a b) = k
type (Arrow k a b) :% Fls Source #
Instance details Defined in Data.Category.Boolean type (Arrow k a b) :% Fls = a
type (Arrow k a b) :% Tru Source #
Instance details Defined in Data.Category.Boolean type (Arrow k a b) :% Tru = b