Complete Boolean Algebras are Bousfield Lattices
Given a complete Heyting algebra, we construct an algebraic tensor triangulated category whose Bousfield lattice is the Booleanization of the given Heyting algebra. As a consequence, we deduce that any complete Boolean algebra is the Bousfield lattice of some tensor triangulated category. Using the same ideas, we then give two further examples illustrating some interesting behaviour of the Bousfield lattice.
I am thankful to the referee for their careful reading of the manuscript; they provided several helpful comments which resulted in improvements to the exposition.
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