Adjunctions between Boolean spaces and skew Boolean algebras

Details Adjunctions between Boolean spaces and skew Boolean algebras Adjunctions between Boolean spaces and skew Boolean algebras

2011-08-29

arxiv.org/abs/1108.5741v1

Mathematics

Category Theory

18 pages

Scientific paper

We apply the representation theory of left-handed skew Boolean algebras by sections of their dual \'{e}tale spaces, given in \cite{K}, to construct a series of dual adjunctions between the categories of locally compact Boolean spaces and left-handed skew Boolean algebras by means of extensions of certain enriched $\Hom$-set functors induced by objects sitting in two categories. The constructed adjunctions are "deformations" of Stone duality obtained by the replacement in the latter of the category of Boolean algebras by the category of left-handed skew Boolean algebras. The constructions provide natural settings for the $\omega$-functor constructed in \cite{LS} and its left adjoint functor.

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