The Popescu-Gabriel theorem for triangulated categories

Details The Popescu-Gabriel theorem for triangulated categories The Popescu-Gabriel theorem for triangulated categories

2007-06-29

arxiv.org/abs/0706.4458v2

Mathematics

K-Theory and Homology

32 pages; submitted to Advances in Mathematics; one reference added

Scientific paper

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.

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