Quantales of open groupoids

DOI10.4171/JNCG/90zbMath1253.06019arXiv0811.4539MaRDI QIDQ426730

Pedro Resende, M. Clarence Protin

Publication date: 12 June 2012

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.4539

zbMATH Keywords

Lie groupoidinverse semigrouptopological groupoidquantalelocalic groupoidopen groupoidpseudogroup

Mathematics Subject Classification ID

Frames, locales (06D22) Topological groupoids (including differentiable and Lie groupoids) (22A22) Inverse semigroups (20M18) Quantales (06F07) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Related Items (13)

Open maps of involutive quantales ⋮ The Involutive Quantaloid of Completely Distributive Lattices ⋮ Quantales and Fell bundles ⋮ The many groupoids of a stably Gelfand quantale ⋮ Relational representation of groupoid quantales ⋮ Actions of étale-covered groupoids ⋮ Quantum B-algebras ⋮ Groupoid sheaves as quantale sheaves ⋮ Groupoid quantales: A non-étale setting ⋮ Effective equivalence relations and principal quantales ⋮ Functoriality of groupoid quantales. II ⋮ Morita equivalence of pseudogroups ⋮ Functoriality of groupoid quantales. I.

Cites Work

• Noncommutative Cartan subalgebras of C*-algebras
• Differentiable stacks and gerbes
• Étale groupoids and their quantales
• Sheaves as modules
• Groupoids, inverse semigroups, and their operator algebras
• An extension of the Galois theory of Grothendieck
• Cartan subalgebras in C*-algebras
• The point of pointless topology
• Étale groupoids as germ groupoids and their base extensions
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