arxiv: 1201.6650 · v2 · pith:UCDXBJEInew · submitted 2012-01-31 · 🧮 math.CT · math.GN

Exponential Kleisli monoids as Eilenberg-Moore algebras

Dirk Hofmann , Fr\'ed\'eric Mynard , Gavin J. Seal This is my paper

classification 🧮 math.CT math.GN

keywords categorykleislimonoidsexponentiablelatticemonoidalstructurethose

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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.

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Exponential Kleisli monoids as Eilenberg-Moore algebras

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