Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics)

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.

• Algebraic Geometry (Graduate Texts in Mathematics)
• Algebraic Topology
• An Introduction to Homological Algebra (Universitext)
• Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics)
• A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics)
• Categories for the Working Mathematician (Graduate Texts in Mathematics)
• Representation Theory: A First Course (Graduate Texts in Mathematics)
• Differential Forms in Algebraic Topology (Graduate Texts in Mathematics)
• Commutative Ring Theory (Cambridge Studies in Advanced Mathematics)
• Riemannian Geometry