Functoriality of groupoid quantales. II
arXiv:1803.01075 · doi:10.1007/s10485-021-09628-y
Abstract
Taking advantage of the quantale-theoretic description of étale groupoids we study principal bundles, Hilsum-Skandalis maps, and Morita equivalence in terms 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.
52 pages. Version 2 contains some improvements in presentation, and a fifth item was added to Corollary 5.20
References in corpus (10)
- Etale groupoids and their quantales
- Stability and invariants of Hilsum-Skandalis maps
- On quantales that classify C*-algebras
- Groupoids in categories with pretopology
- Strong Morita Equivalence of Inverse Semigroups
- Functoriality of groupoid quantales. I
- An algebraic generalization of Kripke structures
- The many groupoids of a stably Gelfand quantale
- Morita equivalence of pseudogroups
- Actions of étale-covered groupoids