| Safe Haskell | Safe-Infered |
|---|
Control.Category.Multiplicative
Description
This module contains Multiplicative and Comultiplicative type classes,
which provide a generalization of splitP and joinP to arbitrary monoidal
categories.
- class Monoidal k p => Multiplicative k p where
- class Monoidal k p => Comultiplicative k p where
Documentation
class Monoidal k p => Multiplicative k p whereSource
Monoidal category with a multiplication natural transformation.
A multiplicative structure on k is the same thing as a monoid object
structure on the identity functor, when End(k) is given the pointwise
monoidal structure.
Laws:
first unit . mult = idl second unit . mult = idr mult . first mult = mult . second mult . associate
Instances
| Monad m => Multiplicative (PipeC m r) Either |
class Monoidal k p => Comultiplicative k p whereSource
Comonoidal category with a comultiplication natural transformation.
A comultiplicative structure on k is the same thing as a coalgebra object
structure on the identity functor, when End(k) is given the pointwise
comonoidal structure.
Laws:
first counit . comult = coidl second counit . comult = coidr first diag . diag = disassociate . second diag . diag
Instances
| Monad m => Comultiplicative (PipeC m r) Either |