Book: Higher Operads, Higher Categories

Book: Higher Operads, Higher Categories

[Tom Leinster]

Fifteen months ago I announced to the list that my book,

   Higher Operads, Higher Categories,

was available on the web.  It is now out in traditional form too, in
the blue-green LMS Lecture Note Series (Cambridge University Press).
Details of both versions can be found at

   http://www.maths.gla.ac.uk/~tl/book.html

The free web version will remain available permanently.

Those of you who came to my talk at CT04 will know that there is a
mistake on the front cover: take out your blue-green Tippex and paint
over the words "Edited by".

Tom

Book: Higher Operads, Higher Categories

[Tom LEINSTER]

Dear Colleagues,

I'm very happy to announce the availability of my book,

"Higher Operads, Higher Categories".

It is available electronically now, and will appear in traditional print
form later in the year.  The electronic version is at

http://arxiv.org/abs/math.CT/0305049

and the nice bound version is

Tom Leinster,
Higher Operads, Higher Categories,
London Mathematical Society Lecture Notes Series,
Cambridge University Press,
ISBN 0-521-53215-9.

Details of the latter will appear at the CUP website (www.cambridge.org),
and it can also be pre-ordered from the usual on-line book stores.

The existence of the electronic version is by arrangement with CUP, more
on which below; first, some mathematical details.


SUMMARY

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.


CONTENTS

Diagram of interdependence
Acknowledgements
Introduction
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

Appendices

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

Bibliography
Glossary of notation
Index


The arrangement with CUP is that I can post a "preprint" version of the
book on the archive now, and then one year after the book has been
published in traditional form, I can update the archive version to agree
with it.  All I've done in return is to give up my royalties (10% of the
profit; there goes my fortune).  This is something of an experiment on
CUP's part: they initially said that it would hurt their sales too much to
have a free electronic version available, then I tried to persuade them
that it might actually help sales, not hurt them, because of the extra
exposure it would get.  There's also the consideration that a 400-page
printout is unwieldy and the book is low-price, so the incentive for
readers to buy is quite high.

In any case, I think that CUP deserve a great deal of credit for being
willing to try this, and I'd be pleased if those who can afford to bought
a copy rather than just using the printout; this would reflect the
goodwill and perhaps encourage CUP to extend this arrangement to other
authors. It'll be about 30 pounds (45 euros or US$) - and as I said, I
make no money from this.


Tom