Homological algebra

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 292)


This chapter contains the bases of homological algebra which are necessary for the understanding of the rest of this book: categories and functors, triangulated categories, localization, derived categories, ind-objects and pro-objects, Mittag-Leffler condition.

Since it is not possible to present in a single chapter the whole theory with all details, we have left out as an exercise some auxiliary results and we have postponed to Chapter X the theory of t-structures, which is not used until there.

Of course, the reader will also consult with great benefit the (classical) books and papers on this subject, such as Bourbaki [1], Cartan-Eilenberg [1], Freyd [1], Gabriel-Zisman [1], Godement [1], Grothendieck [1], Hilton-Stammbach [1], Iversen [1], MacLane [1], Mitchell [1], Northcott [1], and expecially Deligne [1], Gelfand-Manin [1], Hartshorne [1] and Verdier [2] concerning derived categories.


Abelian Group Exact Sequence Commutative Diagram Simple Complex Full Subcategory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyoto 606Japan
  2. 2.Department of MathematicsUniversity of Paris VIParis Cedex 05France

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