Ebook: Progress in Mathematics: Algebra and Geometry
- Tags: Algebra
- Series: Progress in Mathematics 9
- Year: 1971
- Publisher: Springer US
- Edition: 1
- Language: English
- pdf
This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cate gories and class field theory, in the Algebra part, and of Finsler spaces, structures on differentiable manifolds, and packing, cover ing, etc., in the Geometry part. The literature covered is primar Hy that published in 1964-1967. Contents ALGEBRA CATEGORIES ............... . 3 M. S. Tsalenko and E. G. Shul'geifer § 1. Introduction........... 3 § 2. Foundations of the Theory of Categories . . . . . 4 § 3. Fundamentals of the Theory of Categories . . . . . 6 § 4. Embeddings of Categories ... . . . . . . . . . . . . 14 § 5. Representations of Categories . . . . . . . . . . . . . 16 § 6. Axiomatic Characteristics of Algebraic Categories . . . . . . . . . . . . . . . . . . . . . . . . . . 18 § 7. Reflective Subcategories; Varieties. . . 20 § 8. Radicals in Categories . . . . . . . 24 § 9. Categories with Involution. . . . . . 29 § 10. Universal Algebras in Categories . 30 § 11. Categories with Multiplication . . . 34 § 12. Duality of Functors. .. ....... 37 § 13. Homotopy Theory . . . . .. ........... 39 § 14. Homological Algebra in Categories. . . . . . 41 § 15. Concrete Categories . . . . .. ......... 44 § 16. Generalizations.. . . . . . . 45 Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 CLASS FIELD THEORY. FIELD EXTENSIONS. . . . . . . . 59 S. P. Demushkin 66 Literature Cited vii CONTENTS viii GEOMETRY 75 FINSLER SPACES AND THEIR GENERALIZATIONS ..
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Categories....Pages 3-57
Class Field Theory. Field Extensions....Pages 59-71
Front Matter....Pages 73-73
Finsler Spaces and Their Generalizations....Pages 75-136
Structures On Differentiable Manifolds....Pages 137-207
Packings, Coverings, Partitionings, and Certain Other Distributions in Spaces of Constant Curvature....Pages 209-253
Content:
Front Matter....Pages i-ix
Front Matter....Pages 1-1
Categories....Pages 3-57
Class Field Theory. Field Extensions....Pages 59-71
Front Matter....Pages 73-73
Finsler Spaces and Their Generalizations....Pages 75-136
Structures On Differentiable Manifolds....Pages 137-207
Packings, Coverings, Partitionings, and Certain Other Distributions in Spaces of Constant Curvature....Pages 209-253
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