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t-Structures are Normal Torsion Theories

Titlet-Structures are Normal Torsion Theories
Publication TypeJournal Article
Year of Publication2016
AuthorsFiorenza, D, Loregian, F
JournalApplied Categorical Structures
Volume24
Pagination181–208
Date PublishedApr
ISSN1572-9095
Abstract

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

URLhttps://doi.org/10.1007/s10485-015-9393-z
DOI10.1007/s10485-015-9393-z

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