18: Category theory, homological algebra
The word "category" is used to mean something completely different in general topology.
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
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]