Effective equivalence relations and principal quantales

Abstract

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.

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Correspondence to Pedro Resende.

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Pedro Resende: Work funded by FCT/Portugal through the LisMath program and projects EXCL/MAT-GEO/0222/2012 and PEst-OE/EEI/LA0009/2013.

Communicated by Mark V. Lawson.

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Quijano, J.P., Resende, P. Effective equivalence relations and principal quantales. Semigroup Forum 99, 754–787 (2019). https://doi.org/10.1007/s00233-019-09994-z

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Keywords

  • Open localic groupoids
  • Effective equivalence relations
  • Supported quantales