INVERSION AND LOCALIZATION BY QUOTIENT

Among the classes of morphisms saturated for localization which are ma de invertible in a quotient, we investigate those whose localization f unctor is full. We produce a family of categories such that all the lo calization functors are full. Among these one finds the simplicial cat egory, the cyclic category of A. Connes, more generally, the categorie s of Z. Fiedorowicz and J.-L. Loday associated to the crossed simplici al groups, and the categories of matrices with entries in a field. The n, we describe all the localizations of the category of matrices with entries in a principal ring.