Effective equivalence relations and principal quantales

  • Juan Pablo Quijano
  • Pedro ResendeEmail author
Research Article


Stably supported quantales generalize pseudogroups and provide an algebraic context in which to study the correspondences between inverse semigroups and étale groupoids. Here we study a further generalization where a non-unital version of supported quantale carries the algebraic content of such correspondences to the setting of open groupoids. A notion of principal quantale is introduced which, in the case of groupoid quantales, corresponds precisely to effective equivalence relations.


Open localic groupoids Effective equivalence relations Supported quantales 



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Authors and Affiliations

  1. 1.Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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