UID:
almafu_9958071151302883
Format:
1 online resource (291 pages)
ISBN:
1-281-76869-3
,
9786611768690
,
0-08-087329-4
Series Statement:
Pure and applied mathematics; a series of monographs and textbooks ; 17
Content:
Theory of categories
Note:
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
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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
,
English
Additional Edition:
ISBN 0-12-499250-1
Language:
English
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