Progress in Mathematics

1. Front Matter

   Pages i-ix

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2. Algebra

   1. Front Matter

      Pages 1-1

      PDF

   2. Categories

      • M. S. Tsalenko, E. G. Shul’geifer

      Pages 3-57

   3. Class Field Theory. Field Extensions

      • S. P. Demushkin

      Pages 59-71

3. Geometry

   1. Front Matter

      Pages 73-73

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   2. Finsler Spaces and Their Generalizations

      • V. I. Bliznikas

      Pages 75-136

   3. Structures On Differentiable Manifolds

      • A. P. Shirokov

      Pages 137-207

   4. Packings, Coverings, Partitionings, and Certain Other Distributions in Spaces of Constant Curvature

      • E. P. Baranovskii

      Pages 209-253

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 ..

• algebra
• differentiable manifold
• field
• homotopy
• manifold

• V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, Moscow, Russia

  R. V. Gamkrelidze

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