Coverages on Inverse Semigroups
Rings and Algebras
2020-05-19 v1 Category Theory
Operator Algebras
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.
Cite
@article{arxiv.2005.08714,
title = {Coverages on Inverse Semigroups},
author = {Gilles G. de Castro},
journal= {arXiv preprint arXiv:2005.08714},
year = {2020}
}