Distributive law between monads
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Suppose that (S,μS,ηS) and (T,μT,ηT) are two monads on a category C. Their composite (as functors) ST is not necessarily a monad! Distributive laws give a way to compose two monads in order to obtain a monad.
Formally, a distributive law of the monad S over the monad T is a natural transformation
such that the diagrams
and 
commute.
This law induces a composite monad ST with
- as multiplication: SlT.μSμT,
- as unit: ηSηT.
[edit] See also
[edit] References
- Jon Beck (1969). "Distributive laws". Lecture Notes in Mathematics 80: 119–140.
