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Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series) 1st Edition

1 customer review
ISBN-13: 978-0521532150
ISBN-10: 0521532159
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Editorial Reviews

Book Description

Category theory has experienced a resurgence in popularity recently because of new links with topology and mathematical physics. This book gives a user friendly account of higher order category theory and presents operads and multicategories as a natural language for its study. The author has included necessary background material and applications as well as appendices containing some of the more technical proofs that might have disrupted the flow of the text. This book should be a valuable resource to graduate students and researchers in the field.

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Product Details

  • Series: London Mathematical Society Lecture Note Series (Book 298)
  • Paperback: 448 pages
  • Publisher: Cambridge University Press; 1 edition (August 9, 2004)
  • Language: English
  • ISBN-10: 0521532159
  • ISBN-13: 978-0521532150
  • Product Dimensions: 6 x 1 x 9 inches
  • Shipping Weight: 1.6 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #3,777,863 in Books (See Top 100 in Books)

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11 of 13 people found the following review helpful By Dr. Lee D. Carlson HALL OF FAMEVINE VOICE on September 18, 2004
Format: Paperback Verified Purchase
Structures such as braided monoidal categories, operads, and Hopf algebras are familiar to those who have studied topological quantum field theory, knot theory, string theory, and the renormalization procedure in quantum field theory. This book attempts, and succeeds, in presenting to the interested reader an overview of higher category theory, which subsumes the aforementioned topics. It is not however a book on applications, but instead details the purely mathematical aspects of higher category, clarifying for example the difference between `weak' n-categories and `strict' n-categories. The author though has not written a book in the typical "definition-theorem-proof" style, as he motivates the subject very well, and does not hesitate to use diagrams to get his point across. Indeed, he is careful to point out that the subject is inherently topological in its nature, and that diagrams used to illustrate higher-dimensional structures can be viewed as topological structures. The braided monoidal category that arises in knot theory is a perfect example of this.

The author introduces higher-dimensional category theory as one that uses "higher-dimensional arrows", in analogy to ordinary category as one that uses 1-dimensional arrows. Higher-dimensional category theory or `n-category theory,' is viewed as a generalization of the notion of category. To motivate the concept of a weak n-category, the author reminds the reader of the attempt to prove to what extent the loop group in differential topology is in fact a topological group. The composition of paths in the loop groups is not associative, but rather associative up to homotopy. Associativity does hold in strict n-categories but not in weak n-categories.
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Higher Operads, Higher Categories (London Mathematical Society Lecture Note Series)
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