Pandora.Pattern.Category

Documentation

class Semigroupoid m => Category m where

When providing a new instance, you should ensure it satisfies:
* Left identity: identity . f ≡ f
* Right identity: f . identity ≡ f

Minimal complete definition

identity

Methods

identity :: m a a

(<--------) :: m (m a b) (m a b) infixl 1

(<-------) :: m (m a b) (m a b) infixl 2

(<------) :: m (m a b) (m a b) infixl 3

(<-----) :: m (m a b) (m a b) infixl 4

(<----) :: m (m a b) (m a b) infixl 5

(<---) :: m (m a b) (m a b) infixl 6

(<--) :: m (m a b) (m a b) infixl 7

(-------->) :: m (m a b) (m a b) infixr 1

(------->) :: m (m a b) (m a b) infixr 2

(------>) :: m (m a b) (m a b) infixr 3

(----->) :: m (m a b) (m a b) infixr 4

(---->) :: m (m a b) (m a b) infixr 5

(--->) :: m (m a b) (m a b) infixr 6

(-->) :: m (m a b) (m a b) infixr 7

Instances

Category m => Category (Straight m)

Defined in Pandora.Pattern.Morphism.Straight

Methods

identity :: Straight m a a

(<--------) :: Straight m (Straight m a b) (Straight m a b)

(<-------) :: Straight m (Straight m a b) (Straight m a b)

(<------) :: Straight m (Straight m a b) (Straight m a b)

(<-----) :: Straight m (Straight m a b) (Straight m a b)

(<----) :: Straight m (Straight m a b) (Straight m a b)

(<---) :: Straight m (Straight m a b) (Straight m a b)

(<--) :: Straight m (Straight m a b) (Straight m a b)

(-------->) :: Straight m (Straight m a b) (Straight m a b)

(------->) :: Straight m (Straight m a b) (Straight m a b)

(------>) :: Straight m (Straight m a b) (Straight m a b)

(----->) :: Straight m (Straight m a b) (Straight m a b)

(---->) :: Straight m (Straight m a b) (Straight m a b)

(--->) :: Straight m (Straight m a b) (Straight m a b)

(-->) :: Straight m (Straight m a b) (Straight m a b)

Category m => Category (Flip m)

Defined in Pandora.Pattern.Morphism.Flip

Methods

identity :: Flip m a a

(<--------) :: Flip m (Flip m a b) (Flip m a b)

(<-------) :: Flip m (Flip m a b) (Flip m a b)

(<------) :: Flip m (Flip m a b) (Flip m a b)

(<-----) :: Flip m (Flip m a b) (Flip m a b)

(<----) :: Flip m (Flip m a b) (Flip m a b)

(<---) :: Flip m (Flip m a b) (Flip m a b)

(<--) :: Flip m (Flip m a b) (Flip m a b)

(-------->) :: Flip m (Flip m a b) (Flip m a b)

(------->) :: Flip m (Flip m a b) (Flip m a b)

(------>) :: Flip m (Flip m a b) (Flip m a b)

(----->) :: Flip m (Flip m a b) (Flip m a b)

(---->) :: Flip m (Flip m a b) (Flip m a b)

(--->) :: Flip m (Flip m a b) (Flip m a b)

(-->) :: Flip m (Flip m a b) (Flip m a b)

Category (Lens Exactly)

Defined in Pandora.Paradigm.Inventory.Some.Optics

Methods

identity :: Lens Exactly a a

(<--------) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<-------) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<------) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<-----) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<----) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<---) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(<--) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(-------->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(------->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(------>) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(----->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(---->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(--->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

(-->) :: Lens Exactly (Lens Exactly a b) (Lens Exactly a b)

Category (Lens Maybe)

Defined in Pandora.Paradigm.Inventory.Some.Optics

Methods

identity :: Lens Maybe a a

(<--------) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<-------) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<------) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<-----) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<----) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<---) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(<--) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(-------->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(------->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(------>) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(----->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(---->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(--->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

(-->) :: Lens Maybe (Lens Maybe a b) (Lens Maybe a b)

Category ((->) :: Type -> Type -> Type)

Defined in Pandora.Paradigm.Algebraic.Exponential

Methods

identity :: a -> a

(<--------) :: (a -> b) -> (a -> b)

(<-------) :: (a -> b) -> (a -> b)

(<------) :: (a -> b) -> (a -> b)

(<-----) :: (a -> b) -> (a -> b)

(<----) :: (a -> b) -> (a -> b)

(<---) :: (a -> b) -> (a -> b)

(<--) :: (a -> b) -> (a -> b)

(-------->) :: (a -> b) -> (a -> b)

(------->) :: (a -> b) -> (a -> b)

(------>) :: (a -> b) -> (a -> b)

(----->) :: (a -> b) -> (a -> b)

(---->) :: (a -> b) -> (a -> b)

(--->) :: (a -> b) -> (a -> b)

(-->) :: (a -> b) -> (a -> b)