A P-theorem for Inverse Semigroupoids through Ordered Globalizations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912374330490880 |
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| author | Tasca, Felipe Augusto Demeneghi, Paulinho Marín, Víctor Velasco, Willian Goulart Gomes |
| author_facet | Tasca, Felipe Augusto Demeneghi, Paulinho Marín, Víctor Velasco, Willian Goulart Gomes |
| contents | We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue of McAlister triples. As a consequence, we obtain a multi-object version of the P-theorem: every E-unitary inverse semigroupoid is isomorphic to a semidirect product arising from an ordered partial action of a groupoid on a multi-object version of a semilattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A P-theorem for Inverse Semigroupoids through Ordered Globalizations Tasca, Felipe Augusto Demeneghi, Paulinho Marín, Víctor Velasco, Willian Goulart Gomes Category Theory Group Theory Rings and Algebras 18B40 (Primary) 20M30 (Secondary) We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a globalization. This result is used to establish a connection between ordered partial actions of groupoids and a multi-object analogue of McAlister triples. As a consequence, we obtain a multi-object version of the P-theorem: every E-unitary inverse semigroupoid is isomorphic to a semidirect product arising from an ordered partial action of a groupoid on a multi-object version of a semilattice. |
| title | A P-theorem for Inverse Semigroupoids through Ordered Globalizations |
| topic | Category Theory Group Theory Rings and Algebras 18B40 (Primary) 20M30 (Secondary) |
| url | https://arxiv.org/abs/2505.08897 |