zbMATH — the first resource for mathematics

The derived category of an exact category. (English) Zbl 0753.18004
For a saturated (i.e. every idempotent splits) exact category \(\mathcal E\) the derived category \(D({\mathcal E})\) is constructed as the quotient of the homotopy category of chain complexes of objects of \(\mathcal E\), by the full subcategory of acyclic complexes. The paper contains also some useful remarks on different earlier similar constructions.

18E10 Abelian categories, Grothendieck categories
18E30 Derived categories, triangulated categories (MSC2010)
18G35 Chain complexes (category-theoretic aspects), dg categories
Full Text: DOI
[1] Beilinson, A. A.; Bernstein, J.; Deligne, P., Analyse et topology sur les espaces singuliers, Aste´risque, 100 (1982)
[2] Karoubi, M., Alge‘bres de Clifford etK-theorie, Ann. Sci.E´cole Norm. Sup., 1, 161-270 (1968) · Zbl 0194.24101
[3] Rickard, J., Derived categories and stable equivalence (1987), preprint
[4] Thomason, R. W., Higher algebraicK-theory of schemes and of derived categories (1988), preprint · Zbl 0655.55002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.