A Horizontal Categorification of Gelfand Duality
  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. 
Paolo Bertozzini, Roberto Conti (1), Wicharn Lewkeeratiyutkul (2) ((1)   University of Newcastle, Australia, (2) Chulalongko...