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Coverages on inverse semigroups
Semigroup Forum ( IF 0.7 ) Pub Date : 2020-09-30 , DOI: 10.1007/s00233-020-10134-1
Gilles G. de Castro

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.

中文翻译:

逆半群的覆盖

首先,我们给出了一个比 Lawson 和 Lenz 给出的定义弱的逆半群上的覆盖定义,并推广了 Johnstone 给出的半格上覆盖的定义。给定这样的覆盖范围,我们证明存在一个通用的伪群,因为它将覆盖到连接的幂等纯映射转换为幂等纯伪群同态。然后,我们展示了如何从伪群上的一个核到相应 groupoids 的拓扑 groupoid 嵌入。最后,我们应用发现的结果来研究 Exel 的紧过滤器和紧组群的概念。
更新日期:2020-09-30
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