| Copyright | 2008-2010 Edward Kmett |
|---|---|
| License | BSD |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | experimental |
| Portability | non-portable (class-associated types) |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Control.Category.Cartesian
Contents
Description
- class (Symmetric k (Product k), Monoidal k (Product k)) => Cartesian k where
- bimapProduct :: Cartesian k => k a c -> k b d -> Product k a b `k` Product k c d
- braidProduct :: Cartesian k => k (Product k a b) (Product k b a)
- associateProduct :: Cartesian k => Product k (Product k a b) c `k` Product k a (Product k b c)
- disassociateProduct :: Cartesian k => Product k a (Product k b c) `k` Product k (Product k a b) c
- class (Monoidal k (Sum k), Symmetric k (Sum k)) => CoCartesian k where
- bimapSum :: CoCartesian k => k a c -> k b d -> Sum k a b `k` Sum k c d
- braidSum :: CoCartesian k => Sum k a b `k` Sum k b a
- associateSum :: CoCartesian k => Sum k (Sum k a b) c `k` Sum k a (Sum k b c)
- disassociateSum :: CoCartesian k => Sum k a (Sum k b c) `k` Sum k (Sum k a b) c
(Co)Cartesian categories
class (Symmetric k (Product k), Monoidal k (Product k)) => Cartesian k where Source
Minimum definition:
fst, snd, diag fst, snd, (&&&)
Methods
fst :: Product k a b `k` a Source
snd :: Product k a b `k` b Source
diag :: a `k` Product k a a Source
(&&&) :: (a `k` b) -> (a `k` c) -> a `k` Product k b c infixr 3 Source
Instances
| Cartesian (->) |
bimapProduct :: Cartesian k => k a c -> k b d -> Product k a b `k` Product k c d Source
braidProduct :: Cartesian k => k (Product k a b) (Product k b a) Source
associateProduct :: Cartesian k => Product k (Product k a b) c `k` Product k a (Product k b c) Source
free construction of Associative for the product Bifunctor Product k
disassociateProduct :: Cartesian k => Product k a (Product k b c) `k` Product k (Product k a b) c Source
free construction of Disassociative for the product Bifunctor Product k
class (Monoidal k (Sum k), Symmetric k (Sum k)) => CoCartesian k where Source
Instances
| CoCartesian (->) |
bimapSum :: CoCartesian k => k a c -> k b d -> Sum k a b `k` Sum k c d Source
braidSum :: CoCartesian k => Sum k a b `k` Sum k b a Source
associateSum :: CoCartesian k => Sum k (Sum k a b) c `k` Sum k a (Sum k b c) Source
free construction of Associative for the coproduct Bifunctor Sum k
disassociateSum :: CoCartesian k => Sum k a (Sum k b c) `k` Sum k (Sum k a b) c Source
free construction of Disassociative for the coproduct Bifunctor Sum k