A Horizontal Categorification of Gelfand Duality
Operator Algebras
2011-12-30 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.0812.3601,
title = {A Horizontal Categorification of Gelfand Duality},
author = {Paolo Bertozzini and Roberto Conti and Wicharn Lewkeeratiyutkul},
journal= {arXiv preprint arXiv:0812.3601},
year = {2011}
}
Comments
22 pages, AMS-LaTeX2e, results unchanged, several improvements in the exposition, one section added, to appear in Advances in Mathematics