Browsing by Author "Razafindrakoto, Ando"

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    Monadic Aspects of the Ideal Lattice Functor on the Category of Distributive Lattices
    (Springer Science and Business Media B.V., 2025) Razafindrakoto, Ando
    It 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
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    Neighbourhood operators: additivity, idempotency and convergence
    (Springerlink, 2019) Razafindrakoto, Ando
    We define and discuss the notions of additivity and idempotency for neighbourhood and interior operators. We then propose an order-theoretic description of the notion of convergence that was introduced by D. Holgate and J. Šlapal with the help of these two properties.