In this paper we reinterpret the main results about the spectral categoric; by making use of the theory of sheaves and introducing the notion of ‘variety of preadditive categories’. This approach allows us to visualize the structure of the spectral categories better, to explain the different decompositions of a spectral category (discrete and continuous part [4], type I, II and III [14]) and to give an incisive interpretation to the dimension theory for the objects of a spectral category [7]. Moreover, we give an explicit description of the Grothendieck groups df the dense subcategories of a spectral category. Spectral categories, that is abelian categories with exact direct limits in which every exact sequence splits, naturally arise in the study of injective modules (or, more generally, in the study of the injective objects of any Grothendieck category) and their Krull-Remak-Schmidt-Gabriel decompositions [ 121. They were introduced by Gabriel and Oberst [4], who discovered that any spectral category is the product of a discrete spectral category and a continuous one. Later, on the lines of Kaplansky’s theory of types for A W*-algebras [8], Roos [ 141 discovered that every spectral category can be decomposed into a product of categories of three distinct types (type I, II and III). Finally Goodearl and Boyle [7] constructed a complete and beautiful dimension theory for the objects of a spectral category. The directly finite case of that theory is partially based on ideas of Von Neumann and Loomis. We study the spectral categories by means of the varieties of preadditive categories (their definition is given in Section 1). Essentially a variety of preadditive categories is for a preadditive category [ 121 what a ringed space is for a ring. Ringed spaces have been extensively used by Dauns and Hofmann [l] and Pierce [ 1 l] in the study of Von Neumann (bi)regular rings. Here we study the spectral categories by means of varieties of categories. Given any abelian category %, we construct an associated variety of preadditive categories having the spectrum W[ ‘c’] of the Boolean algebra of all idempotents of the center of (z’ as a basis and suitable quotient