The Popescu-Gabriel theorem for triangulated categories

被引：17
作者：
Porta, Marco [1 ,2 ,3 ]
机构：
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
[2] Univ Paris 07, CNRS, UFR Math, UMR 7586, F-75251 Paris 05, France
[3] Univ Milan, Dipartimento Matemat F Enriques, I-20133 Milan, Italy
来源：
ADVANCES IN MATHEMATICS | 2010年 / 225卷 / 03期
关键词：
Popescu-Gabriel theorem; Localization; DG category; Triangulated category; Algebraic triangulated category; Well generated triangulated category; Derived category; Derived functor; BROWN REPRESENTABILITY; DG CATEGORIES; BOUSFIELD; PROOF;
D O I：
10.1016/j.aim.2010.04.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Popescu-Gabriel theorem states that each Grothendieck abelian category is a localization of a module category. In this paper, we prove an analogue where Grothendieck abelian categories are replaced by triangulated categories which are well generated (in the sense of Neeman) and algebraic (in the sense of Keller). The role of module categories is played by derived categories of small differential graded categories. An analogous result for topological triangulated categories has recently been obtained by A. Heider. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：1669 / 1715
页数：47
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