论文标题
共同结构，作用和合作对
Co-t-structures, cotilting and cotorsion pairs
论文作者
论文摘要
令$ \ mathsf {t} $为三角形类别，使用Shift Foundor $σ\ Colon \ Mathsf {T} \ to \ Mathsf {T} $。假设$（\ Mathsf {a}，\ Mathsf {b}）$是一种带有Coheart $ \ Mathsf {s} =σ\ Mathsf {a} \ cap \ Mathsf {b} $的co-t结构\ Mathsf {B} = \ Mathsf {S} *σ\ Mathsf {S} $，这是一个外部类别。 We show that there is a bijection between co-t-structures $(\mathsf{A}',\mathsf{B}')$ in $\mathsf{T}$ such that $\mathsf{A} \subseteq \mathsf{A}' \subseteq Σ\mathsf{A}$ and complete cotorsion pairs in the extended coheart $ \ mathsf {c} $。 In the case that $\mathsf{T}$ is Hom-finite, $\mathbf{k}$-linear and Krull-Schmidt, we show further that there is a bijection between complete cotorsion pairs in $\mathsf{C}$ and functorially finite torsion pairs in $\mathsf{mod}\, \mathsf{S}$.
Let $\mathsf{T}$ be a triangulated category with shift functor $Σ\colon \mathsf{T} \to \mathsf{T}$. Suppose $(\mathsf{A},\mathsf{B})$ is a co-t-structure with coheart $\mathsf{S} = Σ\mathsf{A} \cap \mathsf{B}$ and extended coheart $\mathsf{C} = Σ^2 \mathsf{A} \cap \mathsf{B} = \mathsf{S} * Σ\mathsf{S}$, which is an extriangulated category. We show that there is a bijection between co-t-structures $(\mathsf{A}',\mathsf{B}')$ in $\mathsf{T}$ such that $\mathsf{A} \subseteq \mathsf{A}' \subseteq Σ\mathsf{A}$ and complete cotorsion pairs in the extended coheart $\mathsf{C}$. In the case that $\mathsf{T}$ is Hom-finite, $\mathbf{k}$-linear and Krull-Schmidt, we show further that there is a bijection between complete cotorsion pairs in $\mathsf{C}$ and functorially finite torsion pairs in $\mathsf{mod}\, \mathsf{S}$.
