The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras is also described. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors.
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Editorial Reviews
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"It is...the ideal text for the working mathematician need- ing a detailed description of the fundamentals of the subject as it exists and is used today; the author has succeeded brilliantly in his avowed intention to break down 'the technological barriers between casual users and experts'." Kenneth A. Brown, Mathematical Reviews
"By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library." Joseph Rotman, Bulletin of the American Mathematical Society
"By collecting, organizing, and presenting both the old and the new in homological algebra, Weibel has performed a valuable service. He has written a book that I am happy to have in my library." Joseph Rotman, Bulletin of the American Mathematical Society
Book Description
The landscape of homological algebra has evolved over the past half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today, including historical connections with topology, regular local rings, and semi-simple Lie algebras.
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16 of 20 people found the following review helpful:
5.0 out of 5 stars
Deeeep!,
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This review is from: An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) (Paperback)
Now Homological Algebra is not a simple subject that can be picked up with only a minimal background. The subject is deep and permeates many different braches of mathematics. If you are thinking of buying this text, then I have two suggestions. First, just buy it. For the price, you will not find another book that is as up to date or as rich in content. Second, ask yourself if you are really ready for this text? What I would do is use Amazon's "Search Inside" in order to check out the first two or three pages of chapter one. If you feel at home with the material presented there, then just buy it. You will not be upset. Well, you may get upset-this book covers a lot of material and at times can be rather overwhelming. Let me stress that the level of comfort with the preliminary material is analogous to a tenured professors level of comfort with, say, Calculus. That is, very comfortable. With respect to the actual text, I am hard pressed to find any negative words. Weibel has set the modern standard and this text is fast becoming the standard from which all other texts will have to model themselves after. The material is presented in small palatable chunks that can be consumed at any time. Just make sure you have a new pencil and couple notebooks handy when you read this text.
16 of 24 people found the following review helpful:
5.0 out of 5 stars
Great homological algebra book!,
This review is from: An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) (Paperback)
This book was absolutely priceless for me while I was doing my qualifying exams and dissertation. Excellently written, with modern notation and applications and a clearly-exposited writing style. I wish all "hard" math books were written like this. Thanks Prof. Weibel
8 of 13 people found the following review helpful:
5.0 out of 5 stars
Long Live the Homoligarchy!,
This review is from: An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics) (Paperback)
This is by far the most accessible and well-written Homological Algebra book I've dealt with. I'm an analyst at heart, so the subject does not in any way come easy to me. However, the exposition in this book greatly shortened the learning curve, and Dr. Weibel provided a plethora of understandable examples and accessible exercises, all of which greatly aided my understanding of the subject.
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Inside This Book
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First Sentence:
Homological algebra is a tool used in several branches of mathematics: algebraic topology, group theory, commutative ring theory, and algebraic geometry come to mind. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
fibrant simplicial set, double subcomplex, universal lifting property, assembly lemma, total tensor product, bisimplicial object, balanced functor, universal central extension, low degree terms, simplicial abelian group, profinite set, octahedral axiom, cyclic object, exact triangle, chain homotopy equivalence, chain subcomplex, cohomological functor, principal derivations, cosimplicial object, simplicial resolution, abelian category, simplicial identities, homology spectral sequence, spectral sequence collapses, filtered category Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Shapiro's Lemma, Snake Lemma, Proof Choose, Composition Theorem, Proof Set, Classical Convergence Theorem, Proof Suppose, Dold-Kan Theorem, Affine Lie, Barr's Theorem, Freyd-Mitchell Embedding Theorem, Goodwillie's Theorem, Proof Fix, Proof Recall, Yoneda Ext, Covering Spaces, Proof Pick, Proof Write, Standard Facts, Whitehead's Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Homological algebra is a tool used in several branches of mathematics: algebraic topology, group theory, commutative ring theory, and algebraic geometry come to mind. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
fibrant simplicial set, double subcomplex, universal lifting property, assembly lemma, total tensor product, bisimplicial object, balanced functor, universal central extension, low degree terms, simplicial abelian group, profinite set, octahedral axiom, cyclic object, exact triangle, chain homotopy equivalence, chain subcomplex, cohomological functor, principal derivations, cosimplicial object, simplicial resolution, abelian category, simplicial identities, homology spectral sequence, spectral sequence collapses, filtered category Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Shapiro's Lemma, Snake Lemma, Proof Choose, Composition Theorem, Proof Set, Classical Convergence Theorem, Proof Suppose, Dold-Kan Theorem, Affine Lie, Barr's Theorem, Freyd-Mitchell Embedding Theorem, Goodwillie's Theorem, Proof Fix, Proof Recall, Yoneda Ext, Covering Spaces, Proof Pick, Proof Write, Standard Facts, Whitehead's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 21
books:
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41
books
cite this book:
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- Profinite Groups, Arithmetic, and Geometry. (AM-67) (Annals of Mathematics Studies) by Stephen S. Shatz in Back Matter
- Algebraic K-Theory (Fields Institute Communications) by Victor P. Snaith in Back Matter
- Homological Dimensions of Modules (CBMS Regional Conference Series in Mathematics) by B. Osofsky in Back Matter
- Ring Theory (Chapman & Hall/CRC Pure and Applied Mathematics) by Kenneth Goodearl in Back Matter
- Commutative Rings by Irving Kaplansky in Back Matter
See all 21 books this book cites
- Doing Mathematics: Convention, Subject, Calculation, Analogy by Martin H. Krieger on 4 pages
- Six Lectures on Commutative Algebra (Progress in Mathematics) by J. Elias on page 292, and Back Matter
- Abelian Varieties, Theta Functions and the Fourier Transform (Cambridge Tracts in Mathematics) by Alexander Polishchuk in Front Matter, and Back Matter
- Central Simple Algebras and Galois Cohomology (Cambridge Studies in Advanced Mathematics) by Philippe Gille in Back Matter
- Monomial Algebras (Chapman & Hall/CRC Pure and Applied Mathematics) by Rafael Villarreal in Back Matter
See all 41 books citing this book
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