## Monad Transformers as Monoid Transformers

Citations: | 2 - 0 self |

### BibTeX

@MISC{Jaskelioff_monadtransformers,

author = {Mauro Jaskelioff},

title = {Monad Transformers as Monoid Transformers},

year = {}

}

### OpenURL

### Abstract

The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting monad. A complication of this approach is that the operations associated to the pre-existing monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system F ω. Here, we recast and extend those results in a category-theoretic setting. We abstract and generalize from monads to monoids (in a monoidal category), and from monad transformers to monoid transformers. The generalization brings more simplicity and clarity, and opens the way for lifting of operations with applicability beyond monads. Key words: Monad, Monoid, Monoidal Category