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Co-t-structures, cotilting and cotorsion pairs

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Co-t-structures, cotilting and cotorsion pairs. / Pauksztello, David; Zvonareva, Alexandra.
In: Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 175, No. 1, 31.07.2023.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Pauksztello, D & Zvonareva, A 2023, 'Co-t-structures, cotilting and cotorsion pairs', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 175, no. 1. https://doi.org/10.1017/S030500412300004X

APA

Pauksztello, D., & Zvonareva, A. (2023). Co-t-structures, cotilting and cotorsion pairs. Mathematical Proceedings of the Cambridge Philosophical Society, 175(1). https://doi.org/10.1017/S030500412300004X

Vancouver

Pauksztello D, Zvonareva A. Co-t-structures, cotilting and cotorsion pairs. Mathematical Proceedings of the Cambridge Philosophical Society. 2023 Jul 31;175(1). Epub 2023 Mar 10. doi: 10.1017/S030500412300004X

Author

Pauksztello, David ; Zvonareva, Alexandra. / Co-t-structures, cotilting and cotorsion pairs. In: Mathematical Proceedings of the Cambridge Philosophical Society. 2023 ; Vol. 175, No. 1.

Bibtex

@article{3c235f9f38904d1e8013838306692b0a,
title = "Co-t-structures, cotilting and cotorsion pairs",
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.",
author = "David Pauksztello and Alexandra Zvonareva",
year = "2023",
month = jul,
day = "31",
doi = "10.1017/S030500412300004X",
language = "English",
volume = "175",
journal = "Mathematical Proceedings of the Cambridge Philosophical Society",
issn = "0305-0041",
publisher = "Cambridge University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Co-t-structures, cotilting and cotorsion pairs

AU - Pauksztello, David

AU - Zvonareva, Alexandra

PY - 2023/7/31

Y1 - 2023/7/31

N2 - 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.

AB - 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.

U2 - 10.1017/S030500412300004X

DO - 10.1017/S030500412300004X

M3 - Journal article

VL - 175

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -