Safe Haskell	None
Language	GHC2024

Proarrow.Category.Bicategory.Bidiscrete

Documentation

data DiscreteK (ob :: OB c) (j :: c) (k :: c) where Source Comments #

Constructors

DK :: forall {c} (ob :: OB c) (j :: c). DiscreteK ob j j

Instances

Instances details

CategoryOf c => Bicategory (DiscreteK ob :: c -> c -> Type) Source Comments #

The bicategory with only identity 1-cells and identity 2-cells between those.

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

Methods

o :: forall {i :: c} (j :: c) (k :: c) (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) (c0 :: DiscreteK ob i j) (d :: DiscreteK ob i j). (a ~> b) -> (c0 ~> d) -> O a c0 ~> O b d Source Comments #

withOb2 :: forall {i :: c} {j :: c} {k :: c} (a :: DiscreteK ob j k) (b :: DiscreteK ob i j) r. (Ob a, Ob b, Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob0 (DiscreteK ob) k) => (Ob (O a b) => r) -> r Source Comments #

withOb0s :: forall {j :: c} {k :: c} (a :: DiscreteK ob j k) r. Ob a => ((Ob0 (DiscreteK ob) j, Ob0 (DiscreteK ob) k) => r) -> r Source Comments #

(\\\) :: forall (i :: c) (j :: c) (ps :: DiscreteK ob i j) (qs :: DiscreteK ob i j) r. ((Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob ps, Ob qs) => r) -> (ps ~> qs) -> r Source Comments #

leftUnitor :: forall {i :: c} {j :: c} (a :: DiscreteK ob i j). (Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob a) => O (I :: DiscreteK ob j j) a ~> a Source Comments #

leftUnitorInv :: forall {i :: c} {j :: c} (a :: DiscreteK ob i j). (Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob a) => a ~> O (I :: DiscreteK ob j j) a Source Comments #

rightUnitor :: forall {i :: c} {j :: c} (a :: DiscreteK ob i j). (Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob a) => O a (I :: DiscreteK ob i i) ~> a Source Comments #

rightUnitorInv :: forall {i :: c} {j :: c} (a :: DiscreteK ob i j). (Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob a) => a ~> O a (I :: DiscreteK ob i i) Source Comments #

associator :: forall {h :: c} {i :: c} {j :: c} {k :: c} (a :: DiscreteK ob j k) (b :: DiscreteK ob i j) (c0 :: DiscreteK ob h i). (Ob0 (DiscreteK ob) h, Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob0 (DiscreteK ob) k, Ob a, Ob b, Ob c0) => O (O a b) c0 ~> O a (O b c0) Source Comments #

associatorInv :: forall {h :: c} {i :: c} {j :: c} {k :: c} (a :: DiscreteK ob j k) (b :: DiscreteK ob i j) (c0 :: DiscreteK ob h i). (Ob0 (DiscreteK ob) h, Ob0 (DiscreteK ob) i, Ob0 (DiscreteK ob) j, Ob0 (DiscreteK ob) k, Ob a, Ob b, Ob c0) => O a (O b c0) ~> O (O a b) c0 Source Comments #

CategoryOf (DiscreteK ob j k) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete type (~>) = Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type

Promonad (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

Methods

id :: forall (a :: DiscreteK ob j k). Ob a => Bidiscrete a a Source Comments #

(.) :: forall (b :: DiscreteK ob j k) (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k). Bidiscrete b c0 -> Bidiscrete a b -> Bidiscrete a c0 Source Comments #

Profunctor (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

Methods

dimap :: forall (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) (d :: DiscreteK ob j k). (c0 ~> a) -> (b ~> d) -> Bidiscrete a b -> Bidiscrete c0 d Source Comments #

(\\) :: forall (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) r. ((Ob a, Ob b) => r) -> Bidiscrete a b -> r Source Comments #

type Ob0 (DiscreteK ob :: c -> c -> Type) (k :: c) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

type Ob0 (DiscreteK ob :: c -> c -> Type) (k :: c) = ob k

type I Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

type I = 'DK :: DiscreteK ob i i

type O ('DK :: DiscreteK ob i i) ('DK :: DiscreteK ob i i) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

type O ('DK :: DiscreteK ob i i) ('DK :: DiscreteK ob i i) = 'DK :: DiscreteK ob i i

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

type (~>) = Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type

type Ob (a :: DiscreteK ob j k) Source Comments #

Instance details

Defined in Proarrow.Category.Bicategory.Bidiscrete

type Ob (a :: DiscreteK ob j k) = (j ~ k, a ~~ ('DK :: DiscreteK ob j j), ob j)

data Bidiscrete (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) where Source Comments #

Constructors

Bidiscrete :: forall {c} (ob :: OB c) (j :: c). ob j => Bidiscrete ('DK :: DiscreteK ob j j) ('DK :: DiscreteK ob j j)

Instances

Instances details

Promonad (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods id :: forall (a :: DiscreteK ob j k). Ob a => Bidiscrete a a Source Comments # (.) :: forall (b :: DiscreteK ob j k) (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k). Bidiscrete b c0 -> Bidiscrete a b -> Bidiscrete a c0 Source Comments #
Profunctor (Bidiscrete :: DiscreteK ob j k -> DiscreteK ob j k -> Type) Source Comments #
Instance details Defined in Proarrow.Category.Bicategory.Bidiscrete Methods dimap :: forall (c0 :: DiscreteK ob j k) (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) (d :: DiscreteK ob j k). (c0 ~> a) -> (b ~> d) -> Bidiscrete a b -> Bidiscrete c0 d Source Comments # (\\) :: forall (a :: DiscreteK ob j k) (b :: DiscreteK ob j k) r. ((Ob a, Ob b) => r) -> Bidiscrete a b -> r Source Comments #