This course note introduces
the reader to the language of categories and to present the basic notions of
homological algebra, first from an elementary point of view, with the notion of
derived functors, next with a more sophisticated approach, with the introduction
of triangulated and derived categories.
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.