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Relational Representation of Groupoid Quantales

Abstract

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present paper have several aspects in common with Jónsson and Tarski’s representation theory for relation algebras (Jónsson and Tarski, Am J Math 74(2):127–162, 1952).

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Correspondence to Alessandra Palmigiano.

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The research of the first author was made possible by the VENI grant 639.031.726 of the Netherlands Organization for Scientific Research (NWO).

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Palmigiano, A., Re, R. Relational Representation of Groupoid Quantales. Order 30, 65–83 (2013). https://doi.org/10.1007/s11083-011-9227-z

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  • DOI: https://doi.org/10.1007/s11083-011-9227-z

Keywords

  • Unital involutive quantale
  • Strongly Gelfand quantale
  • Set groupoid
  • Representation theorem

Mathematics Subject Classifications (2010)

  • 06D05
  • 06D22
  • 06D50
  • 06F07
  • 18B40
  • 20L05
  • 22A22
  • 54D10
  • 54D30
  • 54D80