Acyclic models / Michael Barr.

Format:

Book

Author/Creator:

Barr, Michael.

Series:

CRM monograph series 1065-8599 ; v. 17.

CRM monograph series, 1065-8599 ; v. 17

Language:

English

Subjects (All):

Acyclic models.

Physical Description:

xi, 179 pages : illustrations ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [2002]

Contents:

Chapter 1. Categories 1

2. Definition of category 1

3. Functors 9

4. Natural transformations 12

5. Elements and subobjects 15

6. The Yoneda Lemma 19

7. Pullbacks 22

8. Limits and colimits 26

9. Adjoint functors 35

10. Categories of fractions 38

11. The category of modules 42

Chapter 2. Abelian Categories and Homological Algebra 45

1. Additive categories 45

2. Abelian categories 49

3. Exactness 51

4. Homology 56

5. Module categories 61

6. The Z construction 67

Chapter 3. Chain Complexes and Simplicial Objects 69

1. Mapping cones 69

2. Contractible complexes 72

3. Simplicial objects 76

4. Associated chain complex 80

5. The Dold-Puppe theorem 81

6. Double complexes 82

7. Double simplicial objects 86

8. Homology and cohomology of a morphism 87

Chapter 4. Triples a la Mode de Kan 89

1. Triples and cotriples 89

2. Model induced triples 92

3. Triples on the simplicial category 93

4. Historical Notes 94

Chapter 5. The Main Acyclic Models Theorem 95

1. Acyclic classes 95

2. Properties of acyclic classes 99

3. The main theorem 101

4. Homotopy calculuses of fractions 104

5. Exactness conditions 109

Chapter 6. Cartan-Eilenberg Cohomology 113

1. Beck modules 114

2. The main theorem 119

3. Groups 122

4. Associative algebras 125

5. Lie Algebras 126

Chapter 7. Other Applications in Algebra 131

1. Commutative algebras 131

2. More on cohomology of commutative cohomology 145

3. Shukla cohomology 148

4. The Eilenberg-Zilber theorem 148

Chapter 8. Applications in Topology 151

1. Singular homology 151

2. Covered spaces 156

3. Simplicial homology 160

4. Singular homology of triangulated spaces 161

5. Homology with ordered simplexes 163

6. Application to homology on manifolds 168.

Notes:

Includes bibliographical references (pages 175-176) and index.

ISBN:

0821828770

OCLC:

49421662