释义 |
- See also
- References
{{no footnotes|date=August 2015}}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. However, 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 commute. This law induces a composite monad ST with - as multiplication: ,
- as unit: .
See also References | author = Jon Beck | authorlink = Jonathan Mock Beck | year = 1969 | title = Distributive laws | journal = Lecture Notes in Mathematics | volume = 80 | pages = 119–140 | doi = 10.1007/BFb0083084 | series = Lecture Notes in Mathematics | isbn = 978-3-540-04601-1 |author = Michael Barr and Charles Wells |title = Toposes, Triples and Theories |url = http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf |publisher = Springer-Verlag |year = 1985 |isbn = 0-387-96115-1 |deadurl = yes |archiveurl = https://web.archive.org/web/20110514231306/http://www.case.edu/artsci/math/wells/pub/pdf/ttt.pdf |archivedate = 2011-05-14 |df = }}- {{nlab|id=distributive+law|title=Distributive law}}
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