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t-Structures are Normal Torsion Theories

Applied Categorical Structures volume 24, pages 181–208 (2016)Cite this article

Abstract

We characterize t-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a t-structure 𝔱 on a stable ∞-category C is equivalent to a normal torsion theory 𝔽 on C, i.e. to a factorization system 𝔽 = (𝓔, ℳ) where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

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Authors and Affiliations

  1. Dipartimento di Matematica “Guido Castelnuovo”, Università degli Studi di Roma “la Sapienza”, P.le Aldo Moro 2, 00185, Roma, Italy

    Domenico Fiorenza

  2. SISSA - Scuola Internazionale Superiore di Studi Avanzati, via Bonomea 265, 34136, Trieste, Italy

    Fosco Loregiàn

Authors
  1. Domenico Fiorenza
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  2. Fosco Loregiàn
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Correspondence to Fosco Loregiàn.

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Fiorenza, D., Loregiàn, F. t-Structures are Normal Torsion Theories. Appl Categor Struct 24, 181–208 (2016). https://doi.org/10.1007/s10485-015-9393-z

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Keywords

  • Stable ∞-category
  • Triangulated category
  • t-structure
  • Quasicategory
  • Orthogonal factorization system
  • Torsion theory
  • Stability conditions on triangulated categories

Mathematics Subject Classifications (2010)

  • 18E30
  • 18E35
  • 18A40