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Derived categories of abelian categories. (Des catégories dérivées des catégories abéliennes.) (French) Zbl 0882.18010
Astérisque. 239. Paris: Société Mathématique de France, ix, 253 p. (1996).
This volume contains, published for the first time, the thesis of J.-L. Verdier in which he laid the foundations of derived categories of abelian categories and their homological algebra. This thesis, completed in 1967, was one of the corner stones of Grothendieck’s programme to yield generalized cohomological duality theorems. Triangulated categories were first developed axiomatically in this thesis. Therefore, although other accounts of the material have appeared in the intervening period, this volume will be invaluable as a reference work.
Tragically, Verdier passed away on 25 August, 1989 and this volume is edited by L. Illusie in memoriam.

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
14F20 Étale and other Grothendieck topologies and (co)homologies
55U30 Duality in applied homological algebra and category theory (aspects of algebraic topology)
18-02 Research exposition (monographs, survey articles) pertaining to category theory
18G40 Spectral sequences, hypercohomology
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