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Co-t-structures, cotilting and cotorsion pairs

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

E-pub ahead of print
<mark>Journal publication date</mark>10/03/2023
<mark>Journal</mark>Mathematical Proceedings of the Cambridge Philosophical Society
Number of pages18
Publication StatusE-pub ahead of print
Early online date10/03/23
<mark>Original language</mark>English

Abstract

Let T be a triangulated category with shift functor : T → T. Suppose (A, B) is a
co-t-structure with coheart S = A ∩ B and extended coheart C = 2A ∩ B = S ∗ S,
which is an extriangulated category. We show that there is a bijection between co-t-structures
(A, B) in T such that A ⊆ A ⊆ A 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.
2020 Mathematics Subject Classification: 18G80, 18E40 (Primary); 16E35 (Secondary)