Abstract
We examine an inverse semigroup T in terms of the universal locally constant covering of its classifying topos Open image in new window. In particular, we prove that the fundamental group of Open image in new window 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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