2009/11/21 by George Ciprian Modoi, Modoi, George Ciprian
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.CT #math.RA #msc:18A20 #msc:18E15 #msc:18E35
paper · pdf · doi:10.48550/arxiv.0911.4183
14 pages, uses xy-pic
arxiv created 2009/11/21 · arxiv updated 2009/12/08
In this paper we call generalized lax epimorphism a functor defined on a ring with several objects, with values in an abelian AB5 category, for which the associated restriction functor is fully faithful. We characterize such a functor with the help of a conditioned right cancellation of another, constructed in a canonical way from the initial one. As consequences we deduce a characterization of functors inducing an abelian localization and also a necessary and sufficient condition for a morphism of rings with several objects to induce an equivalence at the level of two localizations of the respective module categories.