Monadic Aspects of the Ideal Lattice Functor on the Category of Distributive Lattices

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dc.contributor.authorRazafindrakoto, Ando
dc.date.accessioned2025-11-06T07:45:17Z
dc.date.available2025-11-06T07:45:17Z
dc.date.issued2025
dc.description.abstractIt is known that the construction of the frame of ideals from a distributive lattice induces a monad whose algebras are precisely the frames and frame homomorphisms. Using the Fakir construction of an idempotent approximation of a monad, we extend B. Jacobs’ results on lax idempotent monads and show that the sequence of monads and comonads generated by successive iterations of this ideal functor on its algebras and coalgebras do not strictly lead to a new category. We further extend this result and provide a new proof of the equivalence between distributive lattices and coherent frames by showing that when the first inductive step in the Fakir construction is the identity monad, then the ambient category is equivalent to the category of free algebras
dc.identifier.citationRazafindrakoto, A. (2025) Monadic Aspects of the Ideal Lattice Functor on the Category of Distributive Lattices. Applied categorical structures. [Online] 33 (4), .
dc.identifier.urihttps://doi.org/10.1007/s10485-025-09811-5
dc.identifier.urihttps://hdl.handle.net/10566/21384
dc.language.isoen
dc.publisherSpringer Science and Business Media B.V.
dc.subjectMonad
dc.subjectAlgebras
dc.subjectDistributive lattices
dc.subjectFrames
dc.subjectContinuous lattices
dc.titleMonadic Aspects of the Ideal Lattice Functor on the Category of Distributive Lattices
dc.typeArticle

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