Dualities induced by cotilting bimodules

This paper looks at the dualities induced by cotilting bimodules, which provide a natural generalization of Morita dualities. One of the main goals of the paper is to show that linear compactness also plays a relevant role in this situation, despite the fact that the subcategories involved in cotilting dualities are usually not as wide and do not have closure properties as good as in the Morita case. Ordinary linear compactness does not behave well in this more general context as, for example, the U-reflexive modules with respect to a cotilting bimodule SUR need not be linearly compact. This motivates the study of three generalizations of linear compactness (relative to the bimodule SUR) which are used, among other things, to characterize U-reflexive torsion-free modules. The paper ends with the construction of a cotilting bimodule as a "dual'' of a tilting one and it is shown that this construction is often well behaved from the point of view of linear compactness.