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 , Cartan-Eilenberg , Freyd , Gabriel-Zisman , Godement , Grothendieck , Hilton-Stammbach , Iversen , MacLane , Mitchell , Northcott , and expecially Deligne , Gelfand-Manin , Hartshorne  and Verdier  concerning derived categories.
KeywordsAbelian Group Exact Sequence Commutative Diagram Simple Complex Full Subcategory
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