Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.Category.Op

Documentation

newtype Op k a b Source #

Constructors

Op
Fields fromOp :: k b a

Instances

Instances details

(con ~ Obj k2, Con' x con, UnCon r con, UnCon l con, con i, Autonomous x i r l k2, Braided x i k2) => Autonomous (x :: k1 -> k1 -> k1) (i :: k1) (l :: k1 -> k1) (r :: k1 -> k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Methods turn :: forall (a :: k). Obj (Op k2) a => Op k2 i (x (l a) a) Source # turn' :: forall (a :: k). Obj (Op k2) a => Op k2 (x a (r a)) i Source #
(con ~ Obj k2, Con' x con, UnCon d con, con i, Compact x i d k2, Braided x i k2) => Compact (x :: k1 -> k1 -> k1) (i :: k1) (d :: k1 -> k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op
Braided x i k2 => Braided (x :: k1 -> k1 -> k1) (i :: k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Methods swap :: forall (a :: k) (b :: k). (Obj (Op k2) a, Obj (Op k2) b) => Op k2 (x a b) (x b a) Source # swap_ :: forall (a :: k) (b :: k). (Obj (Op k2) a, Obj (Op k2) b) => Op k2 (x a b) (x b a) Source #
CoCartesian x i k2 => Cartesian (x :: k1 -> k1 -> k1) (i :: k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Methods exl :: forall (a :: k) (b :: k). O2 (Op k2) a b => Op k2 (x a b) a Source # exr :: forall (a :: k) (b :: k). O2 (Op k2) a b => Op k2 (x a b) b Source # dis :: forall (a :: k). Obj (Op k2) a => Op k2 a i Source # dup :: forall (a :: k). Obj (Op k2) a => Op k2 a (x a a) Source # (▵) :: forall (a :: k) (b :: k) (c :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c) => Op k2 a b -> Op k2 a c -> Op k2 a (x b c) Source #
Cartesian x i k2 => CoCartesian (x :: k1 -> k1 -> k1) (i :: k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Methods inl :: forall (a :: k) (b :: k). O2 (Op k2) a b => Op k2 a (x a b) Source # inr :: forall (a :: k) (b :: k). O2 (Op k2) a b => Op k2 b (x a b) Source # new :: forall (a :: k). Obj (Op k2) a => Op k2 i a Source # jam :: forall (a :: k). Obj (Op k2) a => Op k2 (x a a) a Source # (▿) :: forall (a :: k) (b :: k) (c :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c) => Op k2 b a -> Op k2 c a -> Op k2 (x b c) a Source #
Monoidal x i k2 => Monoidal (x :: k1 -> k1 -> k1) (i :: k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Methods (⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c, Obj (Op k2) d) => Op k2 a b -> Op k2 c d -> Op k2 (x a c) (x b d) Source # assoc :: forall (a :: k) (b :: k) (c :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c) => Op k2 (x (x a b) c) (x a (x b c)) Source # assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c) => Op k2 (x a (x b c)) (x (x a b) c) Source # unitorR :: forall (a :: k). (Obj (Op k2) a, Obj (Op k2) i) => Op k2 a (x a i) Source # unitorR_ :: forall (a :: k). (Obj (Op k2) a, Obj (Op k2) i) => Op k2 (x a i) a Source # unitorL :: forall (a :: k). (Obj (Op k2) a, Obj (Op k2) i) => Op k2 a (x i a) Source # unitorL_ :: forall (a :: k). (Obj (Op k2) a, Obj (Op k2) i) => Op k2 (x i a) a Source #
Symmetric x i k2 => Symmetric (x :: k1 -> k1 -> k1) (i :: k1) (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op
Category k2 => Category (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op Associated Types type Obj (Op k2) :: k -> Constraint Source # Methods (.) :: forall (a :: k) (b :: k) (c :: k). (Obj (Op k2) a, Obj (Op k2) b, Obj (Op k2) c) => Op k2 b c -> Op k2 a b -> Op k2 a c Source # id :: forall (a :: k). Obj (Op k2) a => Op k2 a a Source #
Arbitrary (f b a) => Arbitrary (Op f a b) Source #
Instance details Defined in Algebra.Category.Op Methods arbitrary :: Gen (Op f a b) # shrink :: Op f a b -> [Op f a b] #
Show (f b a) => Show (Op f a b) Source #
Instance details Defined in Algebra.Category.Op Methods showsPrec :: Int -> Op f a b -> ShowS # show :: Op f a b -> String # showList :: [Op f a b] -> ShowS #
Additive (f b a) => Additive (Op f a b) Source #
Instance details Defined in Algebra.Category.Op Methods (+) :: Op f a b -> Op f a b -> Op f a b Source # zero :: Op f a b Source # times :: Natural -> Op f a b -> Op f a b Source #
Group (f b a) => Group (Op f a b) Source #
Instance details Defined in Algebra.Category.Op Methods (-) :: Op f a b -> Op f a b -> Op f a b Source # subtract :: Op f a b -> Op f a b -> Op f a b Source # negate :: Op f a b -> Op f a b Source # mult :: Integer -> Op f a b -> Op f a b Source #
TestEqual (f b a) => TestEqual (Op f a b) Source #
Instance details Defined in Algebra.Category.Op Methods (=.=) :: Op f a b -> Op f a b -> Property Source #
type Obj (Op k2 :: k1 -> k1 -> Type) Source #
Instance details Defined in Algebra.Category.Op type Obj (Op k2 :: k1 -> k1 -> Type) = Obj k2