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2021年4月23日(金) 15:00~16:30
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塚本真由氏(山口大学理学部 数理科学科)
Intervals of s-torsion pairs in extriangulated categories with negative first extensions
In a triangulated category, Happel, Reiten and Smalo provided a construction of new t-structures through torsion pairs in the heart of a given t-structure. This construction induces a bijection between the set of certain t-structures and the set of torsion pairs in the heart. On the other hand, Asai–Pfeifer and Tattar established a bijection for torsion pairs in an abelian category, which is related to tau-tilting theory. In this talk, we introduce the notion of s-torsion pairs in an extriangulated category as a common generalization of t-structures and torsion pairs (in abelian/exact categories). Moreover, we establish a bijection for s-torsion pairs in an extriangulated category which unifies two bijections above. This talk is based on a joint work with Takahide Adachi and Haruhisa Enomoto.