From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2271 Path: news.gmane.org!not-for-mail From: Tom LEINSTER Newsgroups: gmane.science.mathematics.categories Subject: Book: Higher Operads, Higher Categories Date: Thu, 8 May 2003 06:05:11 +0200 (CEST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset="US-ASCII" X-Trace: ger.gmane.org 1241018540 3344 80.91.229.2 (29 Apr 2009 15:22:20 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:20 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu May 8 13:27:19 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 08 May 2003 13:27:19 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19DoEL-00047K-00 for categories-list@mta.ca; Thu, 08 May 2003 13:26:49 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 6 Original-Lines: 114 Xref: news.gmane.org gmane.science.mathematics.categories:2271 Archived-At: 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