2023/03/14 by Takahide Adachi, Adachi, Takahide, Mayu Tsukamoto +1 · 1 citation
Mathematics · #18E10 #18G80 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2303.08125
openalex publication_date 2023/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Extriangulated categories give a simultaneous generalization of triangulated categories and exact categories. In this paper, we study silting subcategories of an extriangulated category. First, we show that a silting subcategory induces a basis of the Grothendieck group of an extriangulated category. Secondly, we introduce the notion of silting mutation and investigate its basic properties. Thirdly, we explore properties of silting subcategories of the subcategory consisting of objects with finite projective dimension. As an application, we can recover Auslander--Reiten's result which gives a bijection between tilting modules and contravariantly finite resolving subcategories with finite projective dimension.