梯度三角矩阵类别

M. Lizbeth Shaid Sandoval Miranda, Valente Santiago Vargas, Edgar O. Velasco Páez
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引用次数: 0

摘要

本文的重点是在微分级数范畴中定义微分级数三角矩阵代数。给定两个类别 $\mathcal{U}$ 和 $\mathcal{T}$ 以及 $M \intext\{DgMod}(\mathcal{U} \otimes \mathcal{T}^{text{op}})$, 我们构造了微分级联三角矩阵类别 $\Lambda := \left(\begin{smallmatrix} & 0 \ M & \mathcal{T}^{text{op}})$.\M & U\end{smallmatrix}\right)$.我们的主要结果是,在dg-comma类别$(\text{DgMod}(\mathcal{T}),\text{GDgMod}(\mathcal{U}))$和类别$\text{DgMod}\left( (\left( (\begin{smallmatrix})))$之间存在着dg-类别的等价性。\M &\mathcal{U} (end{smallmatrix})。\end{smallmatrix}\right)/right)$。这个结果是阿尔丁代数中一个众所周知的结果的扩展(例如,见 [2,III.2].
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Diferential graded triangular matrix categories
This paper focuses on defining an analog of differential-graded triangular matrix algebra in the context of differential-graded categories. Given two dg-categories $\mathcal{U}$ and $\mathcal{T}$ and $M \in \text{DgMod}(\mathcal{U} \otimes \mathcal{T}^{\text{op}})$, we construct the differential graded triangular matrix category $\Lambda := \left( \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix} \right)$. Our main result is that there is an equivalence of dg-categories between the dg-comma category $(\text{DgMod}(\mathcal{T}),\text{GDgMod}(\mathcal{U}))$ and the category $\text{DgMod}\left( \left( \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix} \right)\right)$. This result is an extension of a well-known result for Artin algebras (see, for example, [2,III.2].
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