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Progress in Mathematics

Algebra and Geometry

  • R. V. Gamkrelidze

Part of the Progress in Mathematics book series (PM, volume 9)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Algebra

    1. Front Matter
      Pages 1-1
    2. M. S. Tsalenko, E. G. Shul’geifer
      Pages 3-57
    3. S. P. Demushkin
      Pages 59-71
  3. Geometry

About this book

Introduction

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 ..

Keywords

algebra differentiable manifold field homotopy manifold

Editors and affiliations

  • R. V. Gamkrelidze
    • 1
  1. 1.V. A. Steklov Mathematics InstituteAcademy of Sciences of the USSRMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-3306-7
  • Copyright Information Springer-Verlag US 1971
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-3308-1
  • Online ISBN 978-1-4684-3306-7
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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