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<p>We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a universal 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 <i>P</i>-theorem: every <i>E</i>-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.</p>

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A P-theorem for inverse semigroupoids through ordered globalizations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • Felipe Augusto Tasca,
  • Paulinho Demeneghi,
  • Víctor Marín,
  • Willian Goulart Gomes Velasco

摘要

We prove that every ordered partial action of an inverse semigroupoid on a partially ordered set admits a universal 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.