 categoryextras0.53.6: Various modules and constructs inspired by category theory  Contents  Index 

Control.Category.Associative  Portability  portable  Stability  experimental  Maintainer  Edward Kmett <ekmett@gmail.com> 



Description 
NB: this contradicts another common meaning for an Associative Category, which is one
where the pentagonal condition does not hold, but for which there is an identity.


Synopsis 



Documentation 

class Bifunctor p k k k => Associative k p where 
A category with an associative bifunctor satisfying Mac Lane's pentagonal coherence identity law:
bimap id associate . associate . bimap associate id = associate . associate
  Methods  associate :: k (p (p a b) c) (p a (p b c)) 
  Instances  


class Bifunctor s k k k => Coassociative k s where 
A category with a coassociative bifunctor satisyfing the dual of Mac Lane's pentagonal coherence identity law:
bimap coassociate id . coassociate . bimap id coassociate = coassociate . coassociate
  Methods  coassociate :: k (s a (s b c)) (s (s a b) c) 
  Instances  


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