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 étale groupoids and their quantales (Resende (2007) [10]) to a point-set, non-étale setting.
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