'Individuals hoping to learn about derived categories from the ground up (and willing to commit a significant amount of time to the process) will find that this book provides a solid foundation for the topic. Researchers already familiar with some of the theory may benefit from reading this linear development of derived categories, as it also offers a number of enlightening historical and contextual remarks along the way.' Peder Thompson, Mathematical Reviews
Introduction; 1. Basic facts on categories; 2. Abelian categories and additive functors; 3. Differential graded algebra; 4. Translations and standard triangles; 5. Triangulated categories and functors; 6. Localization of categories; 7. The derived category D(A,M); 8. Derived functors; 9. DG and triangulated bifunctors; 10. Resolving subcategories of K(A,M); 11. Existence of resolutions; 12. Adjunctions, equivalences and cohomological dimension; 13. Dualizing complexes over commutative rings; 14. Perfect and tilting DG modules over NC DG rings; 15. Algebraically graded noncommutative rings; 16. Derived torsion over NC graded rings; 17. Balanced dualizing complexes over NC graded rings; 18. Rigid noncommutative dualizing complexes; References; Index.
