| Title: | Relating ample and biample topological categories with Boolean restriction and range semigroups |
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| Authors: | ID Kudryavtseva, Ganna (Author) |
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| Files: |  PDF - Presentation file, download (1,70 MB)
MD5: F241FB9CF269B3AF04A19648674F6B82
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0001870825002117
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | étale groupoid, étale category, Boolean inverse semigroup, Boolean restriction semigroup, Ehresmann semigroup, non-commutative Stone duality |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.07.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 48 str. |
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| Numbering: | Vol. 474, [article no.] 110313 |
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| PID: | 20.500.12556/DiRROS-22175  |
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| UDC: | 512 |
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| ISSN on article: | 0001-8708 |
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| DOI: | 10.1016/j.aim.2025.110313 |
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| COBISS.SI-ID: | 234994947 |
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| Publication date in DiRROS: | 07.05.2025 |
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| Views: | 441 |
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| Downloads: | 220 |
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