A Horizontal Categorification of Gelfand Duality
arXiv:0812.3601 · doi:10.1016/j.aim.2010.06.025
Abstract
In the setting of C*-categories, we provide a definition of "spectrum" of a commutative full C*-category as a one-dimensional unital saturated Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gelfand duality theorem generalizing the usual Gelfand duality between the categories of commutative unital C*-algebras and compact Hausdorff spaces. Although many of the individual ingredients that appear along the way are well-known, the somehow unconventional way we "glue" them together seems to shed some new light on the subject.
22 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, one section added, to appear in Advances in Mathematics
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Cited by in corpus (9)
- Non-Commutative Geometry, Categories and Quantum Physics
- Modular Theory, Non-Commutative Geometry and Quantum Gravity
- Categorical Non-commutative Geometry
- Unifying graded and parameterised monads
- On Strict Higher C*-categories
- Categorical Operator Algebraic Foundations of Relational Quantum Theory
- Spectral C*-categories and Fell bundles with path-lifting
- Non-commutative fermion mass matrix and gravity
- Spectral Theory on Commutative Krein C*-algebras