  We define a right Cartan-Eilenberg structure on the category of Kan's
combinatorial spectra, and the category of sheaves of such spectra, assuming
some conditions. In both structures, we use the geometric concept of homotopy
equivalence as the strong equivalence. In the case of sheaves, we use local
equivalence as the weak equivalence. This paper is the first step in a
larger-scale program of investigating sheaves of spectra from a geometric
viewpoint.
