An Introduction to Homological Algebra

Cambridge Studies in Advanced Mathematics #38

by Charles A. Weibel

The landscape of homological algebra has evolved over the last 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 are also described. This book is suitable for second or third year graduate students. 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. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.

Genres: Mathematics, Algebra

ebook

First published January 1, 1994

Reviews

[NoName66 · Rating 4 out of 5]

The only bad thing is that it only focuses on abelian category, need some topics of other categories. Finished first 3 chapters and chapter 6

[Chris · Rating 5 out of 5]

I'm an amateur interested in group cohomology, and I came across this book at the perfect time. After Hatcher I was a bit bewildered as to what this whole thing is all about. Weibel cleared up alot of my conceptual confusions and has been a great touchstone working through Brown.

[Jim Gillespie · Rating 4 out of 5]

Best homological algebra book out there! The book would get 5 stars if the last chapter covered the unbounded derived category rather than just the bounded below complexes.

[Han Zhicheng]

Emmm.....it seems this book assumes a lot and is very sketchy in its writing style. I shall deal with Rotman's book first...

[Lulu]

Homological algebra