In their Foreword, Gelfand and Manin divide the history of Homological Algebra into three periods: the rst period ended in the early s, culminating in applications of Ho- logical Algebra to regular local rings. The second period, greatly in uenced by the work of A. Grothendieck and J. Serre, continued through the s; it involves abelian categories and sheaf cohomology.
|Published (Last):||5 October 2011|
|PDF File Size:||1.48 Mb|
|ePub File Size:||14.32 Mb|
|Price:||Free* [*Free Regsitration Required]|
In their Foreword, Gelfand and Manin divide the history of Homological Algebra into three periods: the rst period ended in the early s, culminating in applications of Ho- logical Algebra to regular local rings.
The second period, greatly in uenced by the work of A. Grothendieck and J. Serre, continued through the s; it involves abelian categories and sheaf cohomology. The third period, - volving derived categories and triangulated categories, is still ongoing. Both of these newer books discuss all three periods see also Kashiwara—Schapira, Categories and Sheaves.
The original version of this book discussed the rst period only; this new edition remains at the same introductory level, but it now introduces the second period as well. This change makes sense pe- gogically, for there has been a change in the mathematics population since ; today, virtually all mathematics graduate students have learned so- thing about functors and categories, and so I can now take the categorical viewpoint more seriously.
When I was a graduate student, Homological Algebra was an unpopular subject. The general attitude was that it was a grotesque formalism, boring to learn, and not very useful once one had learned it. Read more.
The final prices may differ from the prices shown due to specifics of VAT rules About this book 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. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented.
Methods of Homological Algebra