Theory of Categories
Published on 1. January 1965
272 pages
978-0-08-087329-9 (ISBN)
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Theory of Categories
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Barry Mitchell
Theory of Categories
Book
11/1965
Academic Press
€86.19
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Content
- Front Cover
- Theory of Categories, Volume 17
- Copyright Page
- Contents
- Preface
- Chapter I. Preliminaries
- Introduction
- 1. Definition
- 2. The Nonobjective Approach
- 3. Examples
- 4. Duality
- 5. Special Morphisms
- 6. Equalizers
- 7. Pullbacks, Pushouts
- 8. Intersections
- 9. Unions
- 10. Images
- 11. Inverse Images
- 12. Zero Objects
- 13. Kernels
- 14. Normality
- 15. Exact Categories
- 16. The 9 Lemma
- 17. Products
- 18. Additive Categories
- 19. Exact Additive Categories
- 20. Abelian Categories
- 21. The Category of Abelian Groups G
- Exercises
- Chapter II. Diagrams and Functors
- Introduction
- 1. Diagrams
- 2. Limits
- 3. Functors
- 4. Preservation Properties of Functors
- 5. Morphism Functors
- 6. Limit Preserving Functors
- 7. Faithful Functors
- 8. Functors of Several Variables
- 9. Natural Transformations
- 10. Equivalence of Categories
- 11. Functor Categories
- 12. Diagrams as Functors
- 13. Categories of Additive Functors
- Modules
- 14. Projectives, Injectives
- 15. Generators
- 16. Small Objects
- Exercises
- Chapter III. Complete Categories
- Introduction
- 1. C1 Categories
- 2. Injective Envelopes
- 3. Existence of Injectives
- Exercises
- Chapter IV. Group Valued Functors
- Introduction
- 1. Metatheorems
- 2. The Group Valued Imbedding Theorem
- 3. An Imbedding for Big Categories
- 4. Characterization of Categories of Modules
- 5. Characterization of Functor Categories
- Exercises
- Chapter V. Adjoint Functors
- Introduction
- 1. Generalities
- 2. Conjugate Transformations
- 3. Existence of Adjoints
- 4. Functor Categories
- 5. Reflections
- 6. Monosubcategories
- 7. Projective Classes
- Exercises
- Chapter VI. Applications of Adjoint Functors
- Introduction
- 1. Application to Limits
- 2. Module-Valued Adjoints
- 3. The Tensor Product
- 4. Functor Categories
- 5. Derived Functors
- 6. The Category of Kernel, Preserving Functors
- 7. The Full Imbedding Theorem
- 8. Complexes
- Exercises
- Chapter VII. Extensions
- Introduction
- 1. Ext1
- 2. The Exact Sequence (Special Case)
- 3. Ext
- 4. The Relation ~
- 5. The Exact Sequence
- 6. Global Dimension
- 7. Appendix: Alternative Description of Ext
- Exercises
- Chapter VIII. Satellites
- Introduction
- 1. Connected Sequences of Functors
- 2. Existence of Satellites
- 3. The Exact Sequence
- 4. Satellites of Group Valued Functors
- 5. Projective Sequences
- 6. Several Variables
- Exercises
- Chapter IX. Global Dimension
- Introduction
- 1. Free Categories
- 2. Polynomial Categories
- 3. Grassmann Categories
- 4. Graded Free Categories
- 5. Graded Polynomial Categories
- 6. Graded Grassmann Categories
- 7. Finite Commutative Diagrams
- 8. Homological Tic Tac Toe
- 9. Normal Subsets
- 10. Dimension for Finite Ordered Sets
- Exercises
- Chapter X. Sheaves
- Introduction
- 1. Preliminaries
- 2. F-Categories
- 3. Associated Sheaves
- 4. Direct Images of Sheaves
- 5. Inverse Images of Sheaves
- 6. Sheaves in Abelian Categories
- 7. Injective Sheaves
- 8. Induced Sheaves
- Exercises
- Bibliography
- Subject Index
