On torsion torsionfree triples

Abstract

We study torsion torsionfree(=TTF) triples in abelian and triangulated categories. (Notice that TTF triples in a triangulated category are essentially in bijection with recollement data for this triangulated category.) In particular, we complete Jans' characterization of split TTF triples on a category of modules, prove a weak version of the Generalized Smashing Conjecture, use homological epimorphisms of differential graded(=dg) categories to give an explicite description of all the TTF triples in the derived category of a k-flat dg category and develope an unbounded approach to Koenig's theorem on recollements of right bounded derived categories of ordinary algebras.

Ph. D. thesis, 184 pages

References in corpus (3)

• Noncommutative localization and chain complexes I. Algebraic K- and L-theory
• Two results from Morita theory of stable model categories
• Towers of recollement and bases for diagram algebras: planar diagrams and a little beyond

Cited by in corpus (19)

• Definability and approximations in triangulated categories
• Lifting and restricting recollement data
• Relative singularity categories II: DG models
• On the uniqueness of stratifications of derived module categories
• Morita theory for stable derivators
• Torsion pairs in categories of modules over a preadditive category
• Recollements and tilting objects
• Parametrizing recollement data
• Singular equivalences and Auslander-Reiten conjecture
• Recollements in stable $\infty$-categories
• Gluing silting objects along recollements of well generated triangulated categories
• Recollements of Module Categories
• Blocks of group algebras are derived simple
• s-Recollements and its localization
• Recollements and stratifying ideals
• Ladders of compactly generated triangulated categories and preprojective algebras
• t-structures on stable infinity-categories
• Recollements induced by good silting objects
• Ladders of recollements, categories of monomorphisms and singularity categories