Graded Lawson-Stone Duality
Abstract
The classical Stone duality associates to each Boolean algebra a topological space consisting of ultrafilters. Lawson's generalisation constructs a dual equivalence of categories of Boolean inverse -semigroups and Hausdorff ample topological groupoids. We further generalise the duality to graded versions of those categories, while allowing larger classes of morphisms, and provide various illustrations.
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