Abstrakt
We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between infinity-tilting objects in complete, cocomplete abelian categories with an injective cogenerator and infinity-cotilting objects in complete, cocomplete abelian categories with a projective generator is constructed.
We also introduce infinity-tilting pairs, consisting of an infinity-tilting object and its infinity-tilting class, and obtain a bijective correspondence between infinity-tilting and infinity-cotilting pairs. Finally, we discuss the related derived equivalences and t-structures.