Safe Haskell	None
Language	GHC2024

Proarrow.Object.Pushout

Contents

Orphan instances

Synopsis

data Cocone (bs :: LIST k) (a :: COPROD k) where
- Coapex :: forall {k} (a1 :: k). Ob a1 => Cocone ('L ('[] :: [k])) ('COPR a1)
- Coleg :: forall {k} (b :: k) (a1 :: k) (bs1 :: [k]). (b ~> a1) -> Cocone ('L bs1) ('COPR a1) -> Cocone ('L (b ': bs1)) ('COPR a1)
data Sink (as :: [k]) where
- Cocone :: forall {k} (as :: [k]) (a :: k). Cocone ('L as) ('COPR a) -> Sink as
class HasCoproducts k => HasPushouts k where
- pushout :: forall (o :: k) (a :: k) (b :: k). (o ~> a) -> (o ~> b) -> Sink '[a, b]
thinPushout :: forall {k} (o :: k) (a :: k) (b :: k). HasCoproducts k => (o ~> a) -> (o ~> b) -> Sink '[a, b]
coequalizer :: forall {k} (a :: k) (b :: k). HasPushouts k => (a ~> b) -> (a ~> b) -> Sink '[b]
cokernel :: forall k (a :: k) (b :: k). (HasPushouts k, HasZeroObject k) => (a ~> b) -> Sink '[b]

Documentation

data Cocone (bs :: LIST k) (a :: COPROD k) where Source Github #

A cocone is a bunch of arrows with a shared target.

Constructors

Coapex :: forall {k} (a1 :: k). Ob a1 => Cocone ('L ('[] :: [k])) ('COPR a1)
Coleg :: forall {k} (b :: k) (a1 :: k) (bs1 :: [k]). (b ~> a1) -> Cocone ('L bs1) ('COPR a1) -> Cocone ('L (b ': bs1)) ('COPR a1)

Instances

Instances details

HasCoproducts k => MonoidalProfunctor (Cocone :: LIST k -> COPROD k -> Type) Source Github #
Instance details Defined in Proarrow.Object.Pushout Methods par0 :: Cocone (Unit :: LIST k) (Unit :: COPROD k) Source Github # par :: forall (x1 :: LIST k) (x2 :: COPROD k) (y1 :: LIST k) (y2 :: COPROD k). Cocone x1 x2 -> Cocone y1 y2 -> Cocone (x1 y1) (x2 y2) Source Github #
CategoryOf k => Profunctor (Cocone :: LIST k -> COPROD k -> Type) Source Github #
Instance details Defined in Proarrow.Object.Pushout Methods dimap :: forall (c :: LIST k) (a :: LIST k) (b :: COPROD k) (d :: COPROD k). (c ~> a) -> (b ~> d) -> Cocone a b -> Cocone c d Source Github # lmap :: forall (c :: LIST k) (a :: LIST k) (b :: COPROD k). (c ~> a) -> Cocone a b -> Cocone c b Source Github # rmap :: forall (b :: COPROD k) (d :: COPROD k) (a :: LIST k). (b ~> d) -> Cocone a b -> Cocone a d Source Github # (\\) :: forall (a :: LIST k) (b :: COPROD k) r. ((Ob a, Ob b) => r) -> Cocone a b -> r Source Github #

data Sink (as :: [k]) where Source Github #

A sink is a cocone, but with the apex type hidden by an existential.

Constructors

Cocone :: forall {k} (as :: [k]) (a :: k). Cocone ('L as) ('COPR a) -> Sink as

class HasCoproducts k => HasPushouts k where Source Github #

Pushouts are an inherently dependently typed concept: The type of the apex object depends on the values of the given arrows. But at runtime we can still calculate the arrows and the type, which we hide behind an existential.

Methods

pushout :: forall (o :: k) (a :: k) (b :: k). (o ~> a) -> (o ~> b) -> Sink '[a, b] Source Github #

Instances

Instances details

HasPushouts BOOL Source Github #
Instance details Defined in Proarrow.Category.Instance.Bool Methods pushout :: forall (o :: BOOL) (a :: BOOL) (b :: BOOL). (o ~> a) -> (o ~> b) -> Sink '[a, b] Source Github #
HasPushouts FINSET Source Github #
Instance details Defined in Proarrow.Category.Instance.FinSet Methods pushout :: forall (o :: FINSET) (a :: FINSET) (b :: FINSET). (o ~> a) -> (o ~> b) -> Sink '[a, b] Source Github #
HasPullbacks k => HasPushouts (OPPOSITE k) Source Github #
Instance details Defined in Proarrow.Object.Pushout Methods pushout :: forall (o :: OPPOSITE k) (a :: OPPOSITE k) (b :: OPPOSITE k). (o ~> a) -> (o ~> b) -> Sink '[a, b] Source Github #

thinPushout :: forall {k} (o :: k) (a :: k) (b :: k). HasCoproducts k => (o ~> a) -> (o ~> b) -> Sink '[a, b] Source Github #

In a thin category, arrows don't carry information, so pushouts are just coproducts.

coequalizer :: forall {k} (a :: k) (b :: k). HasPushouts k => (a ~> b) -> (a ~> b) -> Sink '[b] Source Github #

cokernel :: forall k (a :: k) (b :: k). (HasPushouts k, HasZeroObject k) => (a ~> b) -> Sink '[b] Source Github #

Orphan instances

HasPushouts k => HasPullbacks (OPPOSITE k) Source Github #
Instance details Methods pullback :: forall (o :: OPPOSITE k) (a :: OPPOSITE k) (b :: OPPOSITE k). (a ~> o) -> (b ~> o) -> Cosink '[a, b] Source Github #