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arXiv · 2005.08714

Coverages on Inverse Semigroups

Gilles G. de Castro
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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.

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Gilles G. de Castro. 2020-05-18. Coverages on Inverse Semigroups. https://arxiv.org/abs/2005.08714

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