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2025-08-01 08:32:31

A pair of monads in Topology
Ando Razafindrakoto
https://arxiv.org/abs/2507.23403 https://arxiv.org/pdf/2507.23403

A pair of monads in Topology
In the article \cite{Sim}, H. Simmons describes two monads of interests arising from the dual adjunction between the category of topological spaces and that of (bounded) distributive lattices. These are the open prime filter monad and the ideal lattice monad. It is known that the ideal lattice monad induces the ideal frame comonad on the category of frames. We show that this ideal frame comonad can be paired with the open prime filter monad via the open set-spectrum adjunction. From this, we gi…