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arXiv · 2505.08897

A P-theorem for Inverse Semigroupoids through Ordered Globalizations

Felipe Augusto Tasca·Paulinho Demeneghi·Víctor Marín·Willian Goulart Gomes Velasco
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Abstract

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.

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Felipe Augusto Tasca, Paulinho Demeneghi, Víctor Marín, Willian Goulart Gomes Velasco. 2025-05-13. A P-theorem for Inverse Semigroupoids through Ordered Globalizations. https://arxiv.org/abs/2505.08897

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