An Introduction to Homological Algebra
by Charles A. Weibel · Charles A. Weibel
Graduate textbook covering chain complexes, derived functors, Tor and Ext, spectral sequences, group and Lie algebra cohomology, simplicial methods, and derived categories. Readers learn to compute cohomology with resolutions and spectral sequences, the tools underlying algebraic topology and geometry.
This link may earn us a small commission at no extra cost to you. Affiliate disclosure
More resources on Cohomology
Stacks Project
A collaborative, open-source reference on algebraic geometry run from Columbia University, with thousands of pages building from commutative algebra to schemes and algebraic stacks. Every result has a stable tag, so readers can look up precise statements and complete proofs.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Hatcher's Algebraic Topology (free PDF)
Allen Hatcher's standard graduate textbook, freely downloadable from Cornell, covering fundamental groups, homology, cohomology and homotopy theory, with CW complexes introduced in Chapter 0 and used throughout. Readers learn to build spaces from cells and compute their algebraic invariants.
nLab Cohomology
nLab reference entry defining cohomology in the general framework of homotopy theory and higher category theory, as maps into classifying objects. Relates singular, sheaf, group and generalized cohomology, letting readers see how the classical theories fit one abstract definition.
Milne's Etale Cohomology Notes
J.S. Milne's free lecture notes on étale cohomology, covering étale morphisms, sites and sheaves, cohomology of curves, compact supports, and the Lefschetz trace formula. Readers work toward proofs of the rationality and functional equation in the Weil conjectures.
Elements of Algebraic Topology
Textbook on homology theory built from simplicial complexes, then singular homology, cohomology, duality on manifolds, and the Künneth and universal coefficient theorems. Readers learn to compute homology groups concretely and follow the homological algebra underlying them.