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The Popescu-Gabriel theorem for triangulated categories |
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| Authors: | Marco Porta |
| Institution: | a UFR de Mathématiques, UMR 7586 du CNRS, Case 7012, Université Paris 7, 2 place Jussieu, 75251 Paris Cedex 05, France b Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, v. C. Saldini 50, 20133 Milano, Italy c Ben Gurion University, Department of Mathematics, P.O.B. 653, Beer-Sheva, Israel |
| Abstract: | 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. |
| Keywords: | 18E30 16E45 16D90 |
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