Summary
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.
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© 1990 Springer-Verlag Berlin Heidelberg
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Kashiwara, M., Schapira, P. (1990). Homological algebra. In: Sheaves on Manifolds. Grundlehren der mathematischen Wissenschaften, vol 292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02661-8_3
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DOI: https://doi.org/10.1007/978-3-662-02661-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08082-1
Online ISBN: 978-3-662-02661-8
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