Quotients of the Booleanization of an inverse semigroup
arXiv:2007.14890 · doi:10.1007/978-981-33-4842-4_6
Abstract
We introduce -to-join representations of inverse semigroups which are a relaxation of the notion of a cover-to-join representation. We construct the universal -to-join Booleanization of an inverse semigroup as a weakly meet-preserving quotient of the universal Booleanization and show that all such quotients of arise via -to-join representaions. As an application, we provide groupoid models for the intermediate boundary quotients of the -algebra of a Zappa-Szép product right LCM semigroup by Brownlowe, Ramagge, Robertson and Whittaker.
19 pages