  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.
