%0 Journal Article
%T A Horizontal Categorification of Gelfand Duality
%A Paolo Bertozzini
%A Roberto Conti
%A Wicharn Lewkeeratiyutkul
%J Mathematics
%D 2008
%I arXiv
%R 10.1016/j.aim.2010.06.025
%X 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.
%U http://arxiv.org/abs/0812.3601v2