Simone Virili, Universidad de Murcia
Title:
Morita theory for stable derivators
Abstract:
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≤0∩D≥0 be
its heart, we construct a morphism of prederivators
realt : DerA ⟶D,
where DerA 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.