Categories of projective spaces

Starting with an abelian category A, a natural construction produces a category PA such that, when A is an abelian category of vector spaces, PA is the corresponding category of projective spaces. The process of forming the category PA destroys abelianess, but not completely, and the precise measure of what remains of it gives the possibility to reconstruct A out from PA, and allows to characterize categories of the form PA, for an abelian A (projective categories). The characterization is given in terms of the notion of ''Puppe exact category'' and of an appropriate notion of ''weak biproducts''. The proof of the characterization theorem relies on the theory of ''additive relations''.