20.500.12556/DiRROS-22175 Relating ample and biample topological categories with Boolean restriction and range semigroups We extend the equivalence by Cockett and Garner between restriction monoids and ample categories to the setting of Boolean range semigroups which are non-unital one-object versions of range categories. We show that Boolean range semigroups are equivalent to ample topological categories where the range map $r$ is open, and étale Boolean range semigroups are equivalent to biample topological categories. These results yield the equivalence between étale Boolean range semigroups and Boolean birestriction semigroups and a characterization of when a Boolean restriction semigroup admits a compatible cosupport operation. We also recover the equivalence between Boolean birestriction semigroups and biample topological categories by Kudryavtseva and Lawson. Our technique builds on the usual constructions relating inverse semigroups with ample topological groupoids via germs and slices. étale groupoid étale category Boolean inverse semigroup Boolean restriction semigroup Ehresmann semigroup non-commutative Stone duality étalni grupoid étalna kategorija Booleova inverzna polgrupa Booleova omejitvena polgrupa Ehresmannova polgrupa nekomutativna Stoneova dualnost true false true Angleški jezik Slovenski jezik Neznano 2025-05-07 10:31:30 2025-05-07 10:31:30 2025-10-24 03:50:43 0000-00-00 00:00:00 2025 0 0 48 str. [article no.] 110313 Vol. 474 Jul. 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-07-01 512 0001-8708 10.1016/j.aim.2025.110313 234994947 1-s2.0-S0001870825002117-main.pdf 1-s2.0-S0001870825002117-main.pdf 1 F241FB9CF269B3AF04A19648674F6B82 fdca12c929e0a02077da5937ccade6ed6a3e238fc4e80f451ce13a6a2769ea24 347f2399-2b1e-11f0-963a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=32087 https://www.sciencedirect.com/science/article/pii/S0001870825002117 1 addd9ec2-2b1d-11f0-963a-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=32086 Inštitut za matematiko, fiziko in mehaniko 0 0 0