Bernhard Keller

July 14, 1993

Ann. Scient. Ec. Norm. Sup. 27 (1994), 63 - 102

We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" of a theorem of Freyd's and Gabriel's characterizing module categories among abelian categories. After adapting some homological algebra we go on to prove a "Morita theorem" generalizing results of Rickard. Finally, we develop a formalism for Koszul duality in the sense of Beilinson-Ginzburg-Schechtman in the context of DG augmented categories.
Bernhard Keller, le 6 octobre, 1997.

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