Higher Operads, Higher Categories

How to get it

Higher Operads, Higher Categories was the first book on higher category theory.


How to Get It


You have two options:

Electronic: the book is on the archive as math.CT/0305049. It will remain there permanently.
Paper: the book is now in the shops, as

Tom Leinster, Higher Operads, Higher Categories, London Mathematical Society Lecture Note Series 298, Cambridge University Press (2004), ISBN 0-521-53215-9.

You can order it at the usual online book stores. (Incidentally, it says 'Edited by Tom Leinster' on the front cover, but that's the publisher's mistake: I'm the sole author.)

The existence of the free electronic version is by special arrangement with CUP, who I think deserve credit for their flexibility. You can, of course, encourage them to extend their enlightened attitude to other authors by buying the book in its traditional form: CUP are a non-profit organization, so it is priced as low as it can be, and you might prefer a nice bound copy to a 400-page printout anyway.




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. This is the first book on the subject and lays its foundations.

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.

Many examples are given throughout. There is also an introductory chapter motivating the subject for topologists.




Here are the chapter headings. A more detailed contents list (PostScript) shows the section headings too.

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




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