On torsion torsionfree triples

2008/01/03 by Pedro Nicolás, Nicolas, Pedro · 11 citations
Mathematics · Physics and Astronomy · #16D10 #16S90 #18E30 #18E40 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0801.0507

openalex publication_date 2008/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Morita theory for stable derivators
• t-structures on stable infinity-categories
• Metric completions of triangulated categories from hereditary rings
• Torsion pairs in categories of modules over a preadditive category
• Recollements of Module Categories
• Ladders of compactly generated triangulated categories and preprojective algebras
• Singular equivalences and Auslander-Reiten conjecture
• Recollements in stable ∞-categories
• s-Recollements and its localization
• Relative singularity categories II: DG models

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