Gorenstein objects in triangulated categories
Gorenstein objects in triangulated categories
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DOI：
10.1016/j.jalgebra.2004.07.027
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发表时间：
2004-11
影响因子：
0.9
通讯作者：
J. Asadollahi;Shokrollah Salarian
中科院分区：
文献类型：
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作者：
J. Asadollahi;Shokrollah Salarian
三角范畴是具有自同构Σ的加法范畴C：C→C，称为悬挂函子，以及一类形式为A→B→C→ΣA的C图，称为满足[13，Chapire II，Définition 1.1]公理(Tr1)-(Tr4)的(精确)三角形。三角范畴是由Grothendieck和Verdier在60年代初引入的，作为在交换范畴中进行同调代数的适当框架。自从它们被引入以来，它们在代数几何和同调代数中被证明是非常有用的。这方面的例子可以在对偶理论(HartShorne[8]和Iversen[9])中找到，或者在Bernstein、Beilinson和Deligne[3]关于前轴的基础工作中找到。Hochschild发展了模范畴中的相对同调代数。后来，海勒、巴特勒和霍罗克斯把它发展成具有相对阿贝尔结构的更一般的范畴。它的主要主题由一类扩展的精选组成。Trian-
A triangulated category is an additive category C equipped with an automorphism Σ: C→ C, called the suspension functor, and a class of diagrams in C of the form A→ B→ C→ ΣA, called the (exact) triangles satisfying the axioms (Tr1)–(Tr4) of [13, Chapitre II, Définition 1.1. 1, pp. 93–94].Triangulated categories were introduced by Grothendieck and Verdier in the early sixties as the proper framework for doing homological algebra in an abelian category. Since their introduction, they have turned out quiet useful in algebraic geometry and homological algebra. Examples for this can be found in duality theory (Hartshorne [8] and Iversen [9]) or in the fundamental work on preverse sheaves by Bernstein, Beilinson and Deligne [3]. Hochschild has developed relative homological algebra in categories of modules. Afterwards Heller, Butler and Horrocks developed it in more general categories with a relative abelian structure. Its main theme consists of a selection of a class of extensions. Trian-