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Deriving DG categories. (English) Zbl 0799.18007

The author investigates the derived category of a differential \(\mathbb{Z}\)- graded category.
As applications:
1. a “triangulated analogue” of a theorem of P. Freyd [“Abelian Categories”, Harper & Row (1964; Zbl 0121.021)] and P. Gabriel [Bull. Soc. Math. France 90, 323-448 (1962; Zbl 0201.356)] characterizing module categories among abelian categories is deduced;
2. a “Morita theorem” is proved and a formalism for Koszul duality is developed.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
16D90 Module categories in associative algebras
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
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References:

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