A Horizontal Categorification of Gelfand Duality

Details A Horizontal Categorification of Gelfand Duality A Horizontal Categorification of Gelfand Duality

2008-12-18

arxiv.org/abs/0812.3601v2

Advances in Mathematics, 226 n. 1, 584-607 (2011)

Mathematics

Operator Algebras

22 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, one section added, to appear in Advances in

Scientific paper

10.1016/j.aim.2010.06.025

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.

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