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[Texts]## 18: Category theory, homological algebra |

A

The word "category" is used to mean something completely different in general topology.

- 18A: General theory of categories and functors
- 18B: Special categories
- 18C: Categories and algebraic theories
- 18D: Categories with structure
- 18E: Abelian categories
- 18F: Categories and geometry
- 18G: Homological algebra, see also 13DXX, 16EXX, 55UXX

This is among the smaller areas in the Math Reviews database.

Browse all (old) classifications for this area at the AMS.

A full, wide-ranging text on category theory is by Borceux, Francis: "Handbook of categorical algebra", 3 vol (1: Basic category theory; 2: Categories and structures; 3: Categories of sheaves) (Encyclopedia of Mathematics and its Applications, 50-2.) Cambridge University Press, Cambridge, 1994. 345+443+522 pp. ISBN 0-521-44178-1, 0-521-44179-X, 0-521-44180-3 MR96g:18001

Much more informal is MacLane, Saunders: "Categories for the working mathematician", Springer-Verlag, New York-Berlin, 1971

There are a number of textbooks on homological algebra which should be accessible to graduate students in algebra and topology, such as

- Homological algebra, by Henri Cartan and Samuel Eilenberg. Princeton, Princeton University Press, 1956.
- Homology, Saunders Mac Lane. Berlin; New York : Springer-Verlag, c1995.
- An introduction to homological algebra / Joseph J. Rotman. New York: Academic Press, 1979.
- Hilton-Stammbach
- Weibel, Charles A.: "An introduction to homological algebra", Cambridge University Press, Cambridge, 1994. 450 pp. ISBN 0-521-43500-5 MR95f:18001

There is an excellent, if somewhat dated, collection of "Reviews in Topology" by Norman Steenrod, a sorted collection of the relevant reviews from Math Reviews (1940-1967). Many now-classical results date from that period. Several of the sections cover homological algebra well.

Notes for a course in homological algebra [Lee Lady]

- Categories mailing list with links to other sites of interest.
- Here are the AMS and Goettingen resource pages for area 18.

- Tensor product of Z-modules (Abelian groups)
- What is a graded algebra?
- What are spectral sequences? [Tim Chow]
- Can we compute homology groups with Maple? (yes)
- Where do closure operators fit into category theory? (adjoints)
- n-categories (categories, then functors, then natural transformations,...)

Last modified 2004/01/04 by Dave Rusin. Mail: