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The Popescu–Gabriel theorem for triangulated categories

2010; Elsevier BV; Volume: 225; Issue: 3 Linguagem: Inglês

10.1016/j.aim.2010.04.002

1090-2082

Marco Porta,

Advanced Topics in Algebra

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.