Intervals of $s$-torsion pairs in extriangulated categories with negative first extensions
| Autor: | Adachi, Takahide, Enomoto, Haruhisa, Tsukamoto, Mayu |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | As a general framework for the studies of $t$-structures on triangulated categories and torsion pairs in abelian categories, we introduce the notions of extriangulated categories with negative first extensions and $s$-torsion pairs. We define a heart of an interval in the poset of $s$-torsion pairs, which naturally becomes an extriangulated category with a negative first extension. This notion generalizes hearts of $t$-structures on triangulated categories and hearts of twin torsion pairs in abelian categories. In this paper, we show that an interval in the poset of $s$-torsion pairs is bijectively associated with $s$-torsion pairs in the corresponding heart. This bijection unifies two well-known bijections: One is the bijection induced by HRS-tilt of $t$-structures on triangulated categories. The other is Asai--Pfeifer's and Tattar's bijections for torsion pairs in an abelian category, which is related to $\tau$-tilting reduction and brick labeling. Comment: 16 pages |
| Databáze: | arXiv |
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