Ganna Kudryavtseva: Adjunctions between Boolean and skew Boolean algebras

Abstract: Applying the representation of skew Boolean algebras bysections of their dual etale spaces, we construct a series ofadjunctions between the category of locally compact Boolean spacesand the category of skew Boolean algebras, given by enrichedHom-functors. These adjunctions are based on the dual nature offinite sets, that can be looked at as discrete spaces and also asprimitive skew Boolean algebras. Our approach leads to an insight intothe structure of skew Boolean algebras, which enables us to answer theopen questions posed by Leech and Spinks (Skew Boolean algebrasderived from generalized Boolean algebras, Algebra Universalis, 58(2008), no. 3, 287–-302).

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