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Functoriality of Groupoid Quantales. II

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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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Authors and Affiliations

  1. Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    Juan Pablo Quijano & Pedro Resende

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  1. Juan Pablo Quijano
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  2. Pedro Resende
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Correspondence to Juan Pablo Quijano.

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Communicated by Maria Manuel Clementino.

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

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Quijano, J.P., Resende, P. Functoriality of Groupoid Quantales. II. Appl Categor Struct 29, 629–670 (2021). https://doi.org/10.1007/s10485-021-09628-y

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