category-extras-0.53.6: Various modules and constructs inspired by category theoryContentsIndex
Control.Category.Associative
Portabilityportable
Stabilityexperimental
MaintainerEdward 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
class Bifunctor p k k k => Associative k p where
associate :: k (p (p a b) c) (p a (p b c))
class Bifunctor s k k k => Coassociative k s where
coassociate :: k (s a (s b c)) (s (s a b) c)
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))
show/hide 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)
show/hide Instances
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