2021/03/17 by Adachi, Takahide, Enomoto, Haruhisa, Tsukamoto, Mayu · 5 citations
#Category Theory (math.CT) #FOS: Mathematics #Primary 18E40 #Representation Theory (math.RT) #Secondly 18G80
paper · doi:10.48550/arxiv.2103.09549
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 τ-tilting reduction and brick labeling.