Deriving DG categories

  title={Deriving DG categories},
  author={Bernhard Keller},
  journal={Annales Scientifiques De L Ecole Normale Superieure},
  • B. Keller
  • Published 1994
  • Mathematics
  • Annales Scientifiques De L Ecole Normale Superieure
— We investigate the (unbounded) derived category of a differential Z-graded category (=DG category). As a first application, we deduce a "triangulated analogue" (4.3) of a theorem of Freyd's [5], Ex. 5.3 H, and Gabriel's [6], Ch. V, characterizing module categories among abelian categories. After adapting some homological algebra we go on to prove a "Morita theorem" (8.2) generalizing results of [19] and [20]. Finally, we develop a formalism for Koszul duality [1] in the context of DG… 
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  • of Math., Vol. 75
  • 1962