The Booleanization of an inverse semigroup

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)
20 Downloads (Pure)


We prove that the forgetful functor from the category of Boolean inverse semigroups to the category of inverse semigroups with zero has a left adjoint. This left adjoint is what we term the ‘Booleanization’. We establish the exact theoretical connection between the Booleanization of an inverse semigroup and Paterson’s universal groupoid of the inverse semigroup and we explicitly compute the concrete Booleanization of the polycyclic inverse monoid Pn and demonstrate its affiliation with the Cuntz–Toeplitz algebra.
Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalSemigroup Forum
Early online date19 Nov 2019
Publication statusE-pub ahead of print - 19 Nov 2019


  • Boolean algebras
  • Inverse semigroups
  • Stone duality

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'The Booleanization of an inverse semigroup'. Together they form a unique fingerprint.

Cite this