Tuesday, March 3, 14:00, 7.527

Wolfgang Rump, Acyclic closure of an exact category.

Abstract:
The acyclic closure T(A) of an exact category A is an exact category with the closure property that exact complexes are acyclic. The localization T(A)/A is triangulated, and all algebraic triangulated categories are subcategories of some T(A)/A. Categories with T(A)=A arise as categories of Gorenstein projectives, as tilting classes, as representation categories over a CM-order, or in connection with non-commutative resolutions or representation dimension. We focus upon tilting categories, and existence of triangle equivalences between derived categories of the first and second kind.