Boolean sets, skew Boolean algebras and a non-commutative Stone duality

DOI10.1007/s00012-015-0361-0zbMath1350.06010arXiv1303.5940OpenAlexW1674993422MaRDI QIDQ2634703

Mark V. Lawson, Ganna Kudryavtseva

Publication date: 18 February 2016

Published in: Algebra Universalis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.5940

zbMATH Keywords

Boolean algebraStone dualityBoolean spaceétalé spaceskew Boolean algebraright normal bandpresheaf of sets

Mathematics Subject Classification ID

Stone spaces (Boolean spaces) and related structures (06E15) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Presheaves and sheaves in general topology (54B40) Generalizations of Boolean algebras (06E75)

Related Items (10)

General non-commutative locally compact locally Hausdorff Stone duality ⋮ Difference-restriction algebras of partial functions with operators: discrete duality and completion ⋮ Boolean sets, skew Boolean algebras and a non-commutative Stone duality ⋮ Difference-restriction algebras of partial functions: axiomatisations and representations ⋮ Free skew Boolean intersection algebras and set partitions ⋮ A non-commutative Priestley duality. ⋮ Noncommutative Pierce duality between Steinberg rings and ample ringoid bundles ⋮ Stone duality for spectral sheaves and the patch monad ⋮ Topological full groups of ample groupoids with applications to graph algebras ⋮ My journey into noncommutative lattices and their theory

Cites Work

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• Boolean sets, skew Boolean algebras and a non-commutative Stone duality
• Skew Boolean algebras
• A NONCOMMUTATIVE GENERALIZATION OF STONE DUALITY
• NON-COMMUTATIVE STONE DUALITY: INVERSE SEMIGROUPS, TOPOLOGICAL GROUPOIDS AND C*-ALGEBRAS
• A DUALIZING OBJECT APPROACH TO NONCOMMUTATIVE STONE DUALITY
• The Categories of Boolean Lattices, Boolean Rings and Boolean Spaces

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