Co-t-structures, cotilting and cotorsion pairs

Pauksztello, David and Zvonareva, Alexandra (2023) Co-t-structures, cotilting and cotorsion pairs. Mathematical Proceedings of the Cambridge Philosophical Society, 175 (1). ISSN 0305-0041

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Abstract

Let T be a triangulated category with shift functor Σ T→T. Suppose (A,B) is a co-t-structure with coheart S=ΣA⊂B and extended coheart C=Σ2A⊂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 classes in mod S.