Tuesday, May 21, 14:00, 7.527
Nico Stein, Resolution and realisation functors.
I will explain how to construct bounded and unbounded realisation functors
of t-structures and resolution functors (=strong weight complex functors) of
w-structures (=co-t-structures=weight structures) for algebraic triangulated
categories. Under suitable assumptions, they yield an adjunction between the
algebraic triangulated category and the derived category of the heart of the
t-structure for adjacent t- and w-structures.
For silting and cosilting complexes, we obtain a connection between the
derived categories of the heart of the associated t-structure and the module
category that generalises the connection on the abelian level described by
the silting and cosilting theorems for two-term complexes.
We also deduce a Morita theorem for derived categories of suitable abelian
categories which include left-complete Grothendieck categories.