Groupoid quantales: A non-étale setting

Alessandra Palmigiano; Riccardo Re

doi:10.1016/j.jpaa.2010.11.005

Groupoid quantales: A non-étale setting

Alessandra Palmigiano^*, Riccardo Re

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	1945-1957
Number of pages	13
Journal	Journal of Pure and Applied Algebra
Volume	215
Issue number	8
DOIs	https://doi.org/10.1016/j.jpaa.2010.11.005
Publication status	Published - 1 Aug 2011
Externally published	Yes

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title = "Groupoid quantales: A non-{\'e}tale setting",

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 {\'e}tale groupoids and their quantales (Resende (2007) [10]) to a point-set, non-{\'e}tale setting.",

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