Inverse Sets and Inverse Correspondences Over Inverse Semigroups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909163912691712 |
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| author | Uchimura, Tomoki |
| author_facet | Uchimura, Tomoki |
| contents | In this paper, we introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert $C^*$-modules and \Ccorrs in the $C^*$-algebra theory. We show that inverse semigroups and inverse correspondences form a bicategory. In this bicategory, two inverse semigroups are equivalent if and only if they are Morita equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06163 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse Sets and Inverse Correspondences Over Inverse Semigroups Uchimura, Tomoki Operator Algebras Category Theory Group Theory Rings and Algebras In this paper, we introduce notions called inverse set and inverse correspondence over inverse semigroups. These are analogies of Hilbert $C^*$-modules and \Ccorrs in the $C^*$-algebra theory. We show that inverse semigroups and inverse correspondences form a bicategory. In this bicategory, two inverse semigroups are equivalent if and only if they are Morita equivalent. |
| title | Inverse Sets and Inverse Correspondences Over Inverse Semigroups |
| topic | Operator Algebras Category Theory Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2404.06163 |