Cotorsion pairs, model category structures, and representation theory
Cotorsion pairs, model category structures, and representation theory
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DOI：
10.1007/s00209-002-0431-9
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发表时间：
2002-11
影响因子：
0.8
通讯作者：
Mark Hovey
中科院分区：
文献类型：
--
作者：
Mark Hovey
我们对阿贝尔范畴上的Quillen模型结构作了一般性的研究。我们发现它们与由Salce [Sal79]引入的缩扭对密切相关，最近由Enochs及其合作者[EJ00]进行了大量研究。这给出了在阿贝尔范畴上构造模型结构的一种方法，我们通过在一个（可能非交换的）Gorenstein环上的模范畴上构造两个模型结构来说明这种方法。这些模型结构的同伦范畴是模表示理论中常用的稳定模范畴的推广。Benson [Ben97]也对这种稳定模类进行了研究。
We make a general study of Quillen model structures on abelian categories. We show that they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have been much studied recently by Enochs and coauthors [EJ00]. This gives a method of constructing model structures on abelian categories, which we illustrate by building two model structures on the category of modules over a (possibly noncommutative) Gorenstein ring. The homotopy category of these model structures is a generalization of the stable module category much used in modular representation theory. This stable module category has also been studied by Benson [Ben97].