Coverages on Inverse Semigroups
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Publication:6340925
DOI10.1007/S00233-020-10134-1arXiv2005.08714MaRDI QIDQ6340925
Publication date: 18 May 2020
Abstract: First we give a definition of a coverage on a inverse semigroup that is weaker than the one gave by a Lawson and Lenz and that generalizes the definition of a coverage on a semilattice given by Johnstone. Given such a coverage, we prove that there exists a pseudogroup that is universal in the sense that it transforms cover-to-join idempotent-pure maps into idempotent-pure pseudogroup homomorphisms. Then, we show how to go from a nucleus on a pseudogroup to a topological groupoid embedding of the corresponding groupoids. Finally, we apply the results found to study Exel's notions of tight filters and tight groupoids.
General theory of (C^*)-algebras (46L05) Topological groupoids (including differentiable and Lie groupoids) (22A22) Inverse semigroups (20M18)
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