Monad compositions ii: Kleisli strength

Authors:
Ernie Manes;Philip Mulry
Affiliations:
Department of mathematics and statistics, university of massachusetts at amherst, u.s.a.;Department of computer science, colgate university, hamilton, new york, 13346, u.s.a. email: pmulry@mail.colgate.edu
Venue:
Mathematical Structures in Computer Science
Year:
2008

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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.