Functoriality of Groupoid Quantale. II

Abstract

Taking advantage of the quantale-theoretic description of étale groupoids we study principal bundles, Hilsum–Skandalis maps, and Morita equivalence by means of modules on inverse quantal frames. The Hilbert module description of quantale sheaves leads naturally to a formulation of Morita equivalence in terms of bimodules that resemble imprimitivity bimodules of C*-algebras.

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Correspondence to Juan Pablo Quijano.

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Work funded by FCT/Portugal through the LisMath Program and Project PEst-OE/EEI/LA0009/2013.

Communicated by Maria Manuel Clementino.

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Quijano, J.P., Resende, P. Functoriality of Groupoid Quantale. II. Appl Categor Struct (2021). https://doi.org/10.1007/s10485-021-09628-y

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Keywords

  • Étale groupoids
  • Inverse quantal frames
  • Sheaves
  • Principal bundles
  • Hilsum–Skandalis maps
  • Morita equivalence

Mathematics Subject Classification

  • 18F15
  • 18F20
  • 18F70
  • 18F75
  • 22A22
  • 55R10