A pair of monads in Topology
Ando Razafindrakoto · Topology Proceedings · 2025
Two monads of interest arise 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 monadinduces the ideal frame comonad on the category of frames. We show that this ideal frame comonad can be paired with the openprime filter monad via the open set-spectrum adjunction. From this, we give a new proof of the equivalence between the categoryof stably compact spaces and that of stably compact frames on one hand, and that of compact Hausdorff spaces and compact regular frames on the other. We show, among other things, how the Čech-Stone compactifications in Pointfree Topology and PointsetTopology relate to each other in this particular context.