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TitleProgress in Mathematics [electronic resource] : Algebra and Geometry / edited by R. V. Gamkrelidze
ImprintBoston, MA : Springer US : Imprint: Springer, 1971
Connect tohttp://dx.doi.org/10.1007/978-1-4684-3306-7
Descript IX, 253 p. online resource

SUMMARY

This volume contains five review articles, two in the Algebra part and three in the Geometry part, surveying the fields of cateยญ gories and class field theory, in the Algebra part, and of Finsler spaces, structures on differentiable manifolds, and packing, coverยญ ing, etc., in the Geometry part. The literature covered is primarยญ Hy that published in 1964-1967. Contents ALGEBRA CATEGORIES ............... . 3 M. S. Tsalenko and E. G. Shul'geifer ยง 1. Introduction........... 3 ยง 2. Foundations of the Theory of Categories . . . . . 4 ยง 3. Fundamentals of the Theory of Categories . . . . . 6 ยง 4. Embeddings of Categories ... . . . . . . . . . . . . 14 ยง 5. Representations of Categories . . . . . . . . . . . . . 16 ยง 6. Axiomatic Characteristics of Algebraic Categories . . . . . . . . . . . . . . . . . . . . . . . . . . 18 ยง 7. Reflective Subcategories; Varieties. . . 20 ยง 8. Radicals in Categories . . . . . . . 24 ยง 9. Categories with Involution. . . . . . 29 ยง 10. Universal Algebras in Categories . 30 ยง 11. Categories with Multiplication . . . 34 ยง 12. Duality of Functors. .. ....... 37 ยง 13. Homotopy Theory . . . . .. ........... 39 ยง 14. Homological Algebra in Categories. . . . . . 41 ยง 15. Concrete Categories . . . . .. ......... 44 ยง 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

Algebra -- Categories -- Class field theory. Field extensions -- Geometry -- Finsler Spaces and their Generalizations -- Structures on Differentiable Manifolds -- Packings, Coverings, Partitionings, and Certain other Distributions in Spaces of Constant Curvature


Mathematics Algebra Mathematical analysis Analysis (Mathematics) Mathematics Algebra Analysis



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