Categories of projective spaces Original Research Article

Starting with an abelian category image, a natural construction produces a category imageimage such that, when image is an abelian category of vector spaces, imageimage is the corresponding category of projective spaces. The process of forming the category imageimage destroys abelianess, but not completely, and the precise measure of what remains of it gives the possibility to reconstruct image out from imageimage, and allows to characterize categories of the form imageimage, for an abelian image (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”.