## Exponential Kleisli Monoids as Eilenberg-Moore Algebras

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.

Published in:
Applied Categorical Structures, 23, 2, 137-157
Year:
2015
Publisher:
Dordrecht, Springer
ISSN:
0927-2852
Keywords:
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