Covered topics are: General
manipulations of complexes, More on Koszul complexes, General manipulations
applied to projective resolutions, Tor, Regular rings, review of Krull
dimension, Regular sequences and Tor, Cohen–Macaulay rings and modules,
Injective and divisible modules, Injective resolutions, A definition of Ext
using injective resolutions, Duality and injective hulls, Gorenstein rings, Bass
numbers.
This note explains
categories for the working homological algebraist, The category of chain
complexes, R Mod, Enough projectives and injectives, Resolutions,
Derived functors, Abelian categories and spectral sequences.