通过三角范畴的重归纳,构建理想的共轭对

Qikai Wang, Haiyan Zhu
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引用次数: 0

摘要

让$(\mathcal{T}',\mathcal{T},\mathcal{T}'')$是一个有边范畴的重元。$\mathcal{T}'$和$\mathcal{T}''$中的两个完全理想簇对可以被$\mathcal{T}$中的一个完全理想簇对所诱导。如果$(\mathcal{I},\mathcal{I}^\perp )$ 和$(\mathcal{J},\mathcal{J}^\perp)$ 是两个完全理想旋回对的内切范畴、那么$(\mathcal{I}\cap\mathcal{J},\langle\mathcal{I}^\perp,\mathcal{J}^perp\rangle)$也是一对完整的理想旋转对。这样,$mathcal{T}$中的一系列理想旋回对可以由$mathcal{T}'$和$mathcal{T}''$中的两个理想旋回对引起。
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Construct ideal cotorsion pairs by recollement of triangulated categories
Let $(\mathcal{T}',\mathcal{T},\mathcal{T}'')$ be a recollement of triangulated categories. Two complete ideal cotorsion pairs in $\mathcal{T}'$ and $\mathcal{T}''$ can be induced by a complete ideal cotorsion pair in $\mathcal{T}$. If $(\mathcal{I},\mathcal{I}^\perp )$ and $(\mathcal{J},\mathcal{J}^\perp)$ are two complete ideal cotorsion pair in triangulated category, then $(\mathcal{I}\cap\mathcal{J},\langle\mathcal{I}^\perp,\mathcal{J}^\perp\rangle)$ is also a complete ideal cotorsion pair. In this way, a series of ideal cotorsion pairs in $\mathcal{T}$ can be induced by two ideal cotorsion pairs in $\mathcal{T}'$ and $\mathcal{T}''$.
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