Control.Category.Cartesian

Contents

• (Co)Cartesian categories

Description

Synopsis

• class (Symmetric k (Product k), Monoidal k (Product k)) => Cartesian k where
  • type Product k :: * -> * -> *
  • fst :: Product k a b `k` a
  • snd :: Product k a b `k` b
  • diag :: a `k` Product k a a
  • (&&&) :: (a `k` b) -> (a `k` c) -> a `k` Product k b c
• 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
  • type Sum k :: * -> * -> *
  • inl :: a `k` Sum k a b
  • inr :: b `k` Sum k a b
  • codiag :: Sum k a a `k` a
  • (|||) :: k a c -> k b c -> Sum k a b `k` c
• 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

fst, snd, diag
fst, snd, (&&&)