Complete Boolean algebras are Bousfield lattices

2017/07/19 by Stevenson, Greg
#Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.06007

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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• Model-completion of varieties of co-Heyting algebras