Cotilting bimodules and their dualities

The Brenner and Butler theorem allows us to read tilting theory as a far reaching generalization of Morita theory, where the equivalence concerns torsion and torsion-free classes rather than the whole module categories. Here we present some steps for a dual theory. First we introduce the notion of a cotilting bimodule (S)U(R) as a dual of a tilting bimodule. Then we show that this theory generalizes Morita dualities: namely, (S)U(R) cogenerates torsion theories in Mod-R and S-Mod, and it defines four functors realizing dualities between nice subcategories of torsion and torsion-free modules, respectively.