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Higher Operads, Higher Categories

Higher Operads, Higher Categories


Part of London Mathematical Society Lecture Note Series

  • Author: Tom Leinster, Institut des Hautes Études Scientifiques, France
  • Date Published: July 2004
  • availability: Available
  • format: Paperback
  • isbn: 9780521532150

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About the Authors
  • Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics, logic, and theoretical computer science. The heart of this book is the language of generalized operads. This is as natural and transparent a language for higher category theory as the language of sheaves is for algebraic geometry, or vector spaces for linear algebra. It is introduced carefully, then used to give simple descriptions of a variety of higher categorical structures. In particular, one possible definition of n-category is discussed in detail, and some common aspects of other possible definitions are established. This is the first book on the subject and lays its foundations. It will appeal to both graduate students and established researchers who wish to become acquainted with this modern branch of mathematics.

    • Subject that is growing in importance due to exciting applications in mathematical physics
    • Author has written user-friendly treatment of subject including background and applications
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    Product details

    • Date Published: July 2004
    • format: Paperback
    • isbn: 9780521532150
    • length: 448 pages
    • dimensions: 229 x 152 x 25 mm
    • weight: 0.65kg
    • contains: 150 b/w illus.
    • availability: Available
  • Table of Contents

    Part I. Background:
    1. Classical categorical structures
    2. Classical operads and multicategories
    3. Notions of monoidal category
    Part II. Operads. 4. Generalized operads and multicategories: basics
    5. Example: fc-multicategories
    6. Generalized operads and multicategories: further theory
    7. Opetopes
    Part III. n-categories:
    8. Globular operads
    9. A definition of weak n-category
    10. Other definitions of weak n-category
    Appendices: A. Symmetric structures
    B. Coherence for monoidal categories
    C. Special Cartesian monads
    D. Free multicategories
    E. Definitions of trees
    F. Free strict n-categories
    G. Initial operad-with-contraction.

  • Author

    Tom Leinster, Institut des Hautes Études Scientifiques, France

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