A Generalisation of the Munn Semigroup
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908702193221632 |
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| author | Tesolin, Francesco |
| author_facet | Tesolin, Francesco |
| contents | To each meet-semilattice $E$ is associated an inverse semigroup $T_{E}$ called the Munn semigroup of $E$. We generalise this construction by replacing the meet-semilattice $E$ by a presheaf of sets $X$ over a meet-semilattice. The inverse semigroup $T_{X}$ that results is called the generalised Munn semigroup. Our construction can be viewed as a generalisation of one due to Zhitomirskiy as well as a restriction of one due to Reilly. We prove that idempotent-separating representations in to the generalised Munn semigroup characterise étale actions of inverse semigroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08835 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Generalisation of the Munn Semigroup Tesolin, Francesco Rings and Algebras Category Theory 20M18, 20M30, 20M50 To each meet-semilattice $E$ is associated an inverse semigroup $T_{E}$ called the Munn semigroup of $E$. We generalise this construction by replacing the meet-semilattice $E$ by a presheaf of sets $X$ over a meet-semilattice. The inverse semigroup $T_{X}$ that results is called the generalised Munn semigroup. Our construction can be viewed as a generalisation of one due to Zhitomirskiy as well as a restriction of one due to Reilly. We prove that idempotent-separating representations in to the generalised Munn semigroup characterise étale actions of inverse semigroups. |
| title | A Generalisation of the Munn Semigroup |
| topic | Rings and Algebras Category Theory 20M18, 20M30, 20M50 |
| url | https://arxiv.org/abs/2512.08835 |