2020/07/13 by David Pauksztello, Pauksztello, David, Alexandra Zvonareva +1 · 1 citation
Mathematics · #16G10 #18E40 #18G80 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2007.06536
openalex publication_date 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let T be a triangulated category with shift functor Σ\colon T → T. Suppose (A,B) is a co-t-structure with coheart S = ΣA ∩ B and extended coheart C = Σ2 A ∩ B = S * ΣS, which is an extriangulated category. We show that there is a bijection between co-t-structures (A',B') in T such that A ⊆ A' ⊆ ΣA and complete cotorsion pairs in the extended coheart C. In the case that T is Hom-finite, k-linear and Krull-Schmidt, we show further that there is a bijection between complete cotorsion pairs in C and functorially finite torsion pairs in mod S.