categories-0.54.1: categories from category-extras

Portabilityportable
Stabilityexperimental
MaintainerEdward Kmett <ekmett@gmail.com>

Control.Category.Associative

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 whereSource

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))Source

Instances

class Bifunctor s k k k => Disassociative k s whereSource

A category with a disassociative bifunctor satisyfing the dual of Mac Lane's pentagonal coherence identity law:

 bimap disassociate id . disassociate . bimap id disassociate = disassociate . disassociate

Methods

disassociate :: k (s a (s b c)) (s (s a b) c)Source

Instances