| Portability | non-portable (class-associated types) |
|---|---|
| Stability | experimental |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
Control.Bifunctor.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.
- class Bifunctor p => Associative p where
- associate :: p (p a b) c -> p a (p b c)
- class Bifunctor s => Coassociative s where
- coassociate :: s a (s b c) -> s (s a b) c
Documentation
class Bifunctor p => Associative 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
Instances
class Bifunctor s => Coassociative s whereSource
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 :: s a (s b c) -> s (s a b) cSource
Instances