In category theory, an abstract branch of mathematics, distributive laws between monads are a way to express abstractly that two algebraic structures distribute one over the other one.
Suppose that and are two monads on a category C. In general, there is no natural monad structure on the composite functor ST. On the other hand, there is a natural monad structure on the functor ST if there is a distributive law of the monad S over the monad T.
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: ,
- as unit: .
Famous quotes containing the word law:
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—George Bernard Shaw (1856–1950)