A Generalization of the Ehresmann-Schein-Nambooripad Theorem to Two-Sided Ehresmann Semigroupoids
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912912800481280 |
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| author | Haag, Rafael Tamusiunas, Thaísa |
| author_facet | Haag, Rafael Tamusiunas, Thaísa |
| contents | We introduce the notion of two-sided Ehresmann semigroupoids and show that they are in correspondence with a specific class of categories, which we call local biordered Ehresmann categories. This correspondence provides a unified generalization of the Ehresmann-Schein-Nambooripad Theorem for both inverse semigroupoids and Ehresmann semigroups. In particular, two-sided restriction semigroupoids form a distinguished subclass of two-sided Ehresmann semigroupoids, and for this case we describe the associated class of categories, extending earlier results for restriction semigroups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_16879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Generalization of the Ehresmann-Schein-Nambooripad Theorem to Two-Sided Ehresmann Semigroupoids Haag, Rafael Tamusiunas, Thaísa Rings and Algebras 20M50 (Primary), 20M75 (Secondary) We introduce the notion of two-sided Ehresmann semigroupoids and show that they are in correspondence with a specific class of categories, which we call local biordered Ehresmann categories. This correspondence provides a unified generalization of the Ehresmann-Schein-Nambooripad Theorem for both inverse semigroupoids and Ehresmann semigroups. In particular, two-sided restriction semigroupoids form a distinguished subclass of two-sided Ehresmann semigroupoids, and for this case we describe the associated class of categories, extending earlier results for restriction semigroups. |
| title | A Generalization of the Ehresmann-Schein-Nambooripad Theorem to Two-Sided Ehresmann Semigroupoids |
| topic | Rings and Algebras 20M50 (Primary), 20M75 (Secondary) |
| url | https://arxiv.org/abs/2602.16879 |