A P-theorem for Inverse Semigroupoids through Ordered Globalizations
Category Theory
2025-05-15 v1 Group Theory
Rings and Algebras
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.
Cite
@article{arxiv.2505.08897,
title = {A P-theorem for Inverse Semigroupoids through Ordered Globalizations},
author = {Felipe Augusto Tasca and Paulinho Demeneghi and Víctor Marín and Willian Goulart Gomes Velasco},
journal= {arXiv preprint arXiv:2505.08897},
year = {2025}
}