Abelian Model Category Theory

James Gillespie is Professor of Mathematics at Ramapo College of New Jersey. His research interests are homological algebra and abstract homotopy theory and he is the author of thirty-five well-cited articles in the area, particularly on topics such as rings and modules, chain complexes, and sheaves.

• Introduction and main examples: 1. Additive and exact categories; 2. Cotorsion pairs; 3. Stable categories from cotorsion pairs; 4. Hovey triples and abelian model structures; 5. The homotopy category of an abelian model structure; 6. The triangulated homotopy category; 7. Derived functors and abelian monoidal model structures; 8. Hereditary model structures; 9. Constructing complete cotorsion pairs; 10. Abelian model structures on chain complexes; 11. Mixed model structures and examples; 12. Cofibrant generation and well-generated homotopy categories; A. Hovey's correspondence for general exact categories; B. Right and left homotopy relations; C. Bibliographical notes; References; Index.