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Tilting theory for extended module categories
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abstract
In extended hearts of bounded $t$-structures on a triangulated category, we provide a Happel-Reiten-Smalo tilting theorem and a characterization for $s$-torsion pairs. Applying these to $m$-extended module categories, we characterize torsion pairs induced by $(m+1)$-term silting complexes. After establishing Auslander-Reiten theory in extended module categories, we introduce $\tau_{[m]}$-tilting pairs and show bijections between $\tau_{[m]}$-tilting pairs, $(m+1)$-term silting complexes, and functorially finite $s$-torsion pairs.
Forward citations
Cited by 3 Pith papers
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Extended heart construction (I): The heart of $n$-cotorsion pairs on triangulated categories
Every n-cotorsion pair on a triangulated category has a heart that is an abelian n-truncated category, carrying compatible pretriangulated and extriangulated structures.
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Extriangulated factorization systems, $s$-torsion pairs and recollements
Extriangulated factorization systems are shown to be equivalent to s-torsion pairs, offering a unified framework that recovers classical torsion pairs and t-structures.
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Higher-dimensional generalization of abelian categories via DG-categories
Abelian n-truncated DG-categories are introduced as a higher-dimensional analogue of abelian categories, with extriangulated homotopy categories and unique factorization of morphisms.
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