ABSTRACT
Tilting modules generalize projective generators and may be characterized either by weakened generating and projectivity conditions or else by equivalences they define between certain subcategories. Dually cotilting modules generalize injective cogenerators and there are again principally two ways to describe them: first by weakened cogenerating and injectivity conditions, and second by dualities they induce between suitable subcategories. In this paper we begin with several characterizations related to the first point of view, and it turns out that for properties of the second type certain finiteness conditions are needed - similar to the situation for Morita dualities for rings.
