The Booleanization of an inverse semigroup
Category Theory
2019-01-23 v2
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 and demonstrate its affiliation with the Cuntz-Toeplitz algebra.
Keywords
Cite
@article{arxiv.1803.10532,
title = {The Booleanization of an inverse semigroup},
author = {Mark V. Lawson},
journal= {arXiv preprint arXiv:1803.10532},
year = {2019}
}
Comments
This is an updated version of the previous paper. Typos where found have been corrected and a new section added that shows how to construct the Booleanization directly from an arbitrary inverse semigroup with zero (without having to use its distributive completion)