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Semigroup Forum

, Volume 85, Issue 2, pp 227–243

First Online: 18 July 2012Received: 05 April 2011Accepted: 03 July 2012

Abstract

To an inverse semigroup, we associate an étale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that this construction provides an adjoint functor to the functor that maps a groupoid to its inverse semigroup of bisections, where we turn étale groupoids into a category using algebraic morphisms. We also discuss how to recover a groupoid from this inverse semigroup.

KeywordsTerminal inverse semigroup action Étale groupoid Groupoid action Bisection Algebraic morphisms of groupoids Spectrum of a semilattice Communicated by Mark V. Lawson.

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Author: Alcides Buss - Ruy Exel - Ralf Meyer

Source: https://link.springer.com/







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