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arXiv · 2512.08835

A Generalisation of the Munn Semigroup

Francesco Tesolin
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Abstract

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 \'etale actions of inverse semigroups.

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Francesco Tesolin. 2025-12-09. A Generalisation of the Munn Semigroup. https://arxiv.org/abs/2512.08835

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