Complete Boolean algebras are Bousfield lattices

Greg Stevenson

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arXiv · 1707.06007

Complete Boolean algebras are Bousfield lattices

Greg Stevenson

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Abstract

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.

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Greg Stevenson. 2017-07-20. Complete Boolean algebras are Bousfield lattices. https://arxiv.org/abs/1707.06007

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