Frobenius pairs in abelian categories
Frobenius pairs in abelian categories
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DOI：
10.1007/s40062-018-0208-4
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发表时间：
2018-05
影响因子：
0.5
通讯作者：
V. Becerril;O. Mendoza;Marco A. Pérez;V. Santiago
中科院分区：
文献类型：
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作者：
V. Becerril;O. Mendoza;Marco A. Pérez;V. Santiago
我们重新Auslander-Buchweitz近似理论，并发现一些关系，与余挠对和模型范畴结构。本文从相对生成元的概念出发，在阿贝尔范畴中引入了左Frobenius对的概念。本文给出了如何从有限分辨维数的对象的子范畴上的投射精确模型结构，通过相对于的厚子范畴的余挠对构造。我们还建立了这些模型结构之间的对应关系，相对余挠对，弗罗贝纽斯对，和Auslander-Buchweitz上下文。这一理论的一些应用的Gorenstein同调代数的背景下，并与完美的余挠对，覆盖子范畴和cotilting模的连接也提出和描述。
We revisit Auslander–Buchweitz approximation theory and find some relations with cotorsion pairs and model category structures. From the notion of relative generators, we introduce the concept of left Frobenius pairsin an abelian category. We show how to construct froma projective exact model structure on, the subcategory of objects inwith finite-resolution dimension, via cotorsion pairs relative to a thick subcategory of. We also establish correspondences between these model structures, relative cotorsion pairs, Frobenius pairs, and Auslander–Buchweitz contexts. Some applications of this theory are given in the context of Gorenstein homological algebra, and connections with perfect cotorsion pairs, covering subcategories and cotilting modules are also presented and described.