We establish a bijective correspondence involving a class of unital involutive quantales and a class of groupoids whose space of units is a sober space. This class includes equivalence relations that arise from group actions. The resulting axiomatization of the class of quantales, as well as the correspondence defined here, extend the theory of etale groupoids and their quantales (Resende (2007) [10]) to a point-set, non-etale setting. (C) 2010 Elsevier BM. All rights reserved.

Groupoid quantales: A non-etale setting

Re, Riccardo
2011-01-01

Abstract

We establish a bijective correspondence involving a class of unital involutive quantales and a class of groupoids whose space of units is a sober space. This class includes equivalence relations that arise from group actions. The resulting axiomatization of the class of quantales, as well as the correspondence defined here, extend the theory of etale groupoids and their quantales (Resende (2007) [10]) to a point-set, non-etale setting. (C) 2010 Elsevier BM. All rights reserved.
2011
Algebra and Number Theory
Palmigiano, Alessandra; Re, Riccardo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2067718
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