A horizontal categorification of Gel'fand duality

Title: A horizontal categorification of Gel'fand duality
Creator: Bertozzini, Paolo; Conti, Roberto; Lewkeeratiyutkul, Wicharn
Relation: Advances in Mathematics Vol. 226, Issue 1, p. 584-607
Publisher Link: http://dx.doi.org/10.1016/j.aim.2010.06.025
Publisher: Elsevier
Resource Type: journal article
Date: 2011
Description: In the setting of C*-categories, we provide a definition of spectrum of a commutative full C*-categories as a one-dimensional unital Fell bundle over a suitable groupoid (equivalence relation) and prove a categorical Gel'fand duality theorem generalizing the usual Gel'fand 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.
Subject: C*-category; Fell bundle; duality; non-commutative geometry
Identifier: http://hdl.handle.net/1959.13/933057
Identifier: uon:11531
Identifier: ISSN:0001-8708
Language: eng
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