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6 papers · 1 filter
Remarks on Morphisms of Spectral Geometries
Paolo Bertozzini, Fred Jaffrennou
Having in view the study of a version of Gel'fand-Neumark duality adapted to the context of Alain Connes' spectral triples, in this very preliminary review, we first present a desc…
Categorical Non-commutative Geometry
Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
The purpose of this short note was to outline the current status, then in 2011, of some research programs aiming at a categorification of parts of A.Connes' non-commutative geometr…
Krein C*-categories
Paolo Bertozzini, Kasemsun Rutamorn
C*-categories are essentially norm-closed *-categories of bounded linear operators between Hilbert spaces. The purpose of this work is to identify suitable axioms defining Krein C*…
A Horizontal Categorification of Gelfand Duality
Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
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…
Non-Commutative Geometry, Categories and Quantum Physics
Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research pro…
A Category of Spectral Triples and Discrete Groups with Length Function
Paolo Bertozzini, Roberto Conti, Wicharn Lewkeeratiyutkul
In the context of A. Connes' spectral triples, a suitable notion of morphism is introduced. Discrete groups with length function provide a natural example for our definitions. A. C…