Introduction to Abelian model structures and Gorenstein homological dimensions /
xxv, 343 pages : illustrations ; 24 cm. - (Monographs and research notes in mathematics ) Content notes : I. Categorical and Algebraic Preliminaries:
1. Universal constructions ;
2. Abelian categories ;
3. Extension functors ;
4. Torsion functors --
II.. Interactions Between Homological Algebra and Homotopy Theory:
5. Model categories ;
6. Cotorsion pairs ;
7. Hovey correspondence --
III. Classical Homological Dimensions and Abelian Model Structures on Chain Complexes:
8. Injective dimensions and model structures ;
9. Projective dimensions and model structures ;
10. Flat dimensions and model structures --
IV. Gorenstein Homological Dimensions and Abelian Model Structures:
11. Gorenstein-projective and Gorenstein-injective objects ;
12. Gorenstein-injective dimensions and model structures ;
13. Gorenstein-projective dimensions and model structures ;
14. Gorenstein-flat dimensions and model structures. Abelian categories.
