Simone Virili, Universidad de Murcia
Morita theory for stable derivators
We give a general construction of realization functors for t-structures on the base of a strong stable derivator. In particular, given such a derivator D, a t-structure t=(D≤0,D≥0) on the triangulated category D(1), and letting A=D≤0D≥0 be its heart,  we construct a morphism of prederivators 


where Der is the natural prederivator enhancing the derived category of A. Furthermore, we give criteria for this morphism to be fully faithful and essentially surjective. If the t-structure t is induced by a suitably "bounded" co/tilting object, realt is an equivalence. Our construction unifies and extends most of the derived co/tilting equivalences appeared in the literature in the last years.