## DERIVING DG CATEGORIES

### 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.

http://www.math.jussieu.fr/~keller/publ/ddcabs.html

Bernhard Keller, le 6 octobre, 1997.

keller@math.jussieu.fr

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