Applied Categorical Structures

, Volume 23, Issue 2, pp 137–157 | Cite as

Exponential Kleisli Monoids as Eilenberg–Moore Algebras

  • Dirk Hofmann
  • Frédéric MynardEmail author
  • Gavin J. Seal


Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.


Exponentiable object Monad Monoidal category Topological category 

Mathematics Subject Classifications (2010)

18C20 18B30 54A05 


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Dirk Hofmann
    • 1
  • Frédéric Mynard
    • 2
    Email author
  • Gavin J. Seal
    • 3
  1. 1.CIDMA, Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  2. 2.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA
  3. 3.Mathematics SectionEcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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