This note covers the following topics: Reflections , Adjoint functors ,
Chain complexes, Homology , Homological algebra, First approximation to derived
functors, Bar resolutions and the classical theory of derived functors, Double
complexes, Long exact sequences, Diagrammatics , The third fundamental lemma,
Generators and cogenerators.
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.