An Introduction to Homological Algebra
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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Review: An Introduction to Homological AlgebraUser Review - Han Zhicheng - Goodreads
Emmm.....it seems this book assumes a lot and is very sketchy in its writing style. I shall deal with Rotman's book first... Read full review
Review: An Introduction to Homological AlgebraUser Review - Jim Gillespie - Goodreads
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. Read full review