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Index
Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
List of Figures
List of Tables
Acknowledgements
Author Biography
I Categorical and algebraic preliminaries
1 Universal constructions
1.1 Introduction
1.2 The opposite category and duality
1.3 Limits and colimits
2 Abelian categories
2.1 Introduction
2.2 Additive categories
2.3 Abelian categories and exact sequences
2.4 Grothendieck categories
3 Extension functors
3.1 Introduction
3.2 Projective and injective objects
3.3 Projective and injective dimensions
3.4 Extension groups via cohomology
3.5 Extension groups via Baer description
3.6 Applications of Baer extensions: adjunction properties for sphere and disk chain complexes
4 Torsion functors
4.1 Introduction
4.2 Monoidal categories
4.3 Closed monoidal categories on chain complexes over a ring
4.4 Derived functors of and
4.5 Flat chain complexes
4.6 Torsion functors and flat dimensions
II Interactions between homological algebra and homotopy theory
5 Model categories
5.1 Introduction
5.2 Weak factorization systems
5.3 Model categories
5.4 The homotopy category of a model category
5.5 Monoidal model categories
6 Cotorsion pairs
6.1 Introduction
6.2 Complete and hereditary cotorsion pairs
6.3 Eklof and Trlifaj Theorem
6.4 Compatible cotorsion pairs
6.5 Induced cotorsion pairs of chain complexes
7 Hovey Correspondence
7.1 Introduction
7.2 Hovey Correspondence
7.3 Abelian factorization systems
7.4 Proof of the Hovey Correspondence
7.5 Abelian model structures on monoidal categories
7.6 Further reading
III Classical homological dimensions and abelian model structures on chain complexes
8 Injective dimensions and model structures
8.1 Introduction
8.2 n-Injective model structures on chain complexes
8.3 Degreewise n-Injective model structures on chain complexes
9 Projective dimensions and model structures
9.1 Introduction
9.2 Projective dimensions and cotorsion pairs of R-modules
9.3 The category of modules over a ringoid
9.4 Projective dimensions of modules over ringoids and special precovers
9.5 n-projective model structures
9.6 Degreewise n-projective model structures
10 Flat dimensions and model structures
10.1 Introduction
10.2 The n-flat modules and cotorsion pairs
10.3 The n-flat cotorsion pair of chain complexes and model structures
10.4 The homotopy category of differential graded model structures
10.5 Degreewise n-flat model structures
10.6 Further reading
IV Gorenstein homological dimensions and abelian model structures
11 Gorenstein-projective and Gorenstein-injective objects
11.1 Introduction
11.2 Properties of Gorenstein-projective and Gorenstein-injective objects
11.3 Gorenstein-projective and Gorenstein-injective dimensions
12 Gorenstein-injective dimensions and model structures
12.1 Introduction
12.2 Gorenstein categories
12.3 Cotorsion pairs from Gorenstein homological dimensions
12.4 Hovey’s model structures on Gorenstein categories
12.5 The Gorenstein n-injective model structure
12.6 Homotopy categories in Gorenstein homological algebra
12.7 Gorenstein-homological dimensions of chain complexes
12.8 Further reading
13 Gorenstein-projective dimensions and model structures
13.1 Introduction
13.2 G-projective dimensions and cotorsion pairs
13.3 Model structures from Gorenstein-projective dimensions
14 Gorenstein-flat dimensions and model structures
14.1 Introduction
14.2 Gorenstein-flat modules
14.3 Gorenstein-flat dimensions
14.4 Gorenstein-flat dimensions of chain complexes
14.5 Gorenstein-homological dimensions of graded modules
14.6 Further reading
Bibliography
Index
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