Methods of Homological Algebra

Sergei I. Gelfand, Yuri I. Manin (Autoren)

Buch | Softcover

XX, 372 Seiten

2010 | 2. Softcover reprint of hardcover 2nd ed. 2003
Springer Berlin (Verlag)
978-3-642-07813-2 (ISBN)

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Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn a modern approach to homological algebra and to use it in their work. For the second edition the authors have made numerous corrections.

I. Simplicial Sets.- II. Main Notions of the Category Theory.- III. Derived Categories and Derived Functors.- IV. Triangulated Categories.- V. Introduction to Homotopic Algebra.- References.

From the reviews of the second edition:

"This is the revised edition of a modern approach to homological algebra by two leading writers in the field. It is based on the systematic use of the language and technics of derived categories and derived functors. The reader has all the basic material and a lot of examples ... . This book can be used by students just beginning to study homological algebra, as well as by specialists who will find there some points which have never been clarified in the literature." (Jean-Claude Thomas, Belgian Mathematical Society - Simon Stevin Bulletin, Vol. 10 (2), 2003)

"It is a pleasure to have on the desk this second edition from a new classical text in mathematics. ... this text has to be seen as part of the general process of unification in mathematics." (Bernd Richter, Zentralblatt MATH, Vol. 1006, 2003)

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XX, 372 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	598 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	category theory • cohomology • Homological algebra • homotopical algebra • sheaf cohomology
ISBN-10	3-642-07813-3 / 3642078133
ISBN-13	978-3-642-07813-2 / 9783642078132
Zustand	Neuware