TY - JOUR
T1 - Groupoid quantales
T2 - A non-étale setting
AU - Palmigiano, Alessandra
AU - Re, Riccardo
PY - 2011/8/1
Y1 - 2011/8/1
N2 - 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.
AB - 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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U2 - 10.1016/j.jpaa.2010.11.005
DO - 10.1016/j.jpaa.2010.11.005
M3 - Article
AN - SCOPUS:79952486654
VL - 215
SP - 1945
EP - 1957
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 8
ER -