Abstract
We examine an inverse semigroup T in terms of the universal locally constant covering of its classifying topos . In particular, we prove that the fundamental group of coincides with the maximum group image of T. We explain the connection between E-unitary inverse semigroups and locally decidable toposes, characterize E-unitary inverse semigroups in terms of a kind of geometric morphism called a spread, characterize F-inverse semigroups, and interpret McAlister’s “P-theorem” in terms of the universal covering.
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Funk, J., Steinberg, B. The Universal Covering of an Inverse Semigroup. Appl Categor Struct 18, 135–163 (2010). https://doi.org/10.1007/s10485-008-9147-2
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DOI: https://doi.org/10.1007/s10485-008-9147-2