Monad compositions ii: Kleisli strength Export

@article{ManesMulry08Compositions, abstract = {In this paper we introduce the concept of Kleisli strength for monads in an arbitrary symmetric monoidal category. This generalises the notion of commutative monad and gives us new examples, even in the cartesian-closed category of sets. We exploit the presence of Kleisli strength to derive methods for generating distributive laws. We also introduce linear equations to extend the results to certain quotient monads. Mechanisms are described for finding strengths that produce a large collection of new distributive laws, and consequently monad compositions, including the composition of monadic data types such as lists, trees, exceptions and state.}, address = {New York, NY, USA}, author = {Manes, Ernie and Mulry, Philip}, citeulike-article-id = {5043048}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=1394793}, citeulike-linkout-1 = {http://dx.doi.org/10.1017/S0960129508006695}, doi = {10.1017/S0960129508006695}, issn = {0960-1295}, journal = {Mathematical. Structures in Comp. Sci.}, keywords = {distributive\_laws, examples\_functors, examples\_monads, monads}, number = {3}, pages = {613--643}, posted-at = {2009-07-02 17:52:17}, priority = {2}, publisher = {Cambridge University Press}, title = {Monad compositions ii: Kleisli strength}, url = {http://dx.doi.org/10.1017/S0960129508006695}, volume = {18}, year = {2008} }

TY - JOUR ID - ManesMulry08Compositions L3 - citeulike-article-id:5043048 N2 - In this paper we introduce the concept of Kleisli strength for monads in an arbitrary symmetric monoidal category. This generalises the notion of commutative monad and gives us new examples, even in the cartesian-closed category of sets. We exploit the presence of Kleisli strength to derive methods for generating distributive laws. We also introduce linear equations to extend the results to certain quotient monads. Mechanisms are described for finding strengths that produce a large collection of new distributive laws, and consequently monad compositions, including the composition of monadic data types such as lists, trees, exceptions and state. IS - 3 JF - Mathematical. Structures in Comp. Sci. SN - 0960-1295 AD - New York, NY, USA EP - 643 TI - Monad compositions ii: Kleisli strength PB - Cambridge University Press VL - 18 SP - 613 KW - distributive_laws KW - examples_functors KW - examples_monads KW - monads AU - Manes, Ernie AU - Mulry, Philip PY - 2008/// UR - http://dx.doi.org/10.1017/S0960129508006695 ER -