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arXiv · 1803.10532

The Booleanization of an inverse semigroup

Mark V. Lawson
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Abstract

We prove that the forgetful functor from the category of Boolean inverse semigroups to inverse semigroups with zero has a left adjoint. This left adjoint is what we term the `Booleanization'. We establish the exact connection between the Booleanization of an inverse semigroup and Paterson's universal groupoid of the inverse semigroup and we explicitly compute the Booleanization of the polycyclic inverse monoid $P_{n}$ and demonstrate its affiliation with the Cuntz-Toeplitz algebra.

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Mark V. Lawson. 2018-03-28. The Booleanization of an inverse semigroup. https://arxiv.org/abs/1803.10532

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