The IMA Volumes in Mathematics and its Applications

Towards Higher Categories

Editors: Baez, John C., May, J. Peter (Eds.)

  • Thorough but informal guide to the theory of higher categorical structures

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eBook $119.00
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  • ISBN 978-1-4419-1524-5
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Hardcover $159.00
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  • ISBN 978-1-4419-1523-8
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Softcover $159.00
price for USA
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  • ISBN 978-1-4614-2463-5
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About this book

The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory.

The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry.

This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.

Table of contents (6 chapters)

  • Lectures on N-Categories and Cohomology

    Baez, John C. (et al.)

    Pages 1-68

  • A Survey of (∞, 1)-Categories

    Bergner, Julia E.

    Pages 69-83

  • Internal Categorical Structures in Homotopical Algebra

    Paoli, Simona

    Pages 85-103

  • A 2-Categories Companion

    Lack, Stephen

    Pages 105-191

  • Notes on 1- and 2-Gerbes

    Breen, Lawrence

    Pages 193-235

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-1-4419-1524-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4419-1523-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4614-2463-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Towards Higher Categories
Editors
  • John C. Baez
  • J. Peter May
Series Title
The IMA Volumes in Mathematics and its Applications
Series Volume
152
Copyright
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4419-1524-5
DOI
10.1007/978-1-4419-1524-5
Hardcover ISBN
978-1-4419-1523-8
Softcover ISBN
978-1-4614-2463-5
Series ISSN
0940-6573
Edition Number
1
Number of Pages
XIII, 283
Topics