Volume: 170; 2016; 428 pp; Hardcover
MSC: Primary 18; 05; 06;
Print ISBN: 978-1-4704-2723-8
Product Code: GSM/170
List Price: $89.00
AMS Member Price: $71.20
MAA Member Price: $80.10
Electronic ISBN: 978-1-4704-2871-6
Product Code: GSM/170.E
List Price: $89.00
AMS Member Price: $71.20
MAA Member Price: $80.10
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Supplemental Materials
Colored Operads
Share this pageDonald Yau
The subject of this book is the theory of
operads and colored operads, sometimes called symmetric
multicategories. A (colored) operad is an abstract object which
encodes operations with multiple inputs and one output and relations
between such operations. The theory originated in the early 1970s in
homotopy theory and quickly became very important in algebraic
topology, algebra, algebraic geometry, and even theoretical physics
(string theory). Topics covered include basic graph theory, basic
category theory, colored operads, and algebras over colored operads.
Free colored operads are discussed in complete detail and in full
generality.
The intended audience of this book includes students and
researchers in mathematics and other sciences where operads and
colored operads are used. The prerequisite for this book is minimal.
Every major concept is thoroughly motivated. There are many graphical
illustrations and about 150 exercises. This book can be used in a
graduate course and for independent study.
Readership
Graduate students and researchers in mathematics and other sciences where operads and colored operads are used.
Reviews & Endorsements
'Colored Operads' has a very low barrier to entry, and so would be suitable even for strong undergraduates. Each chapter has exercises at the end, so this book could form the core of a final-year reading course or project...The organizational aspects of this book are exceptional, with a very thorough List of Notations, a Table of Contents that is fine enough to be very usable without being so long as to discourage perusal, a helpful List of Main Facts giving concise versions of all major theorems, and a good Index. The Bibliography is varied, with good references to a wide literature on operads. Yau's monograph offers a very careful introduction to the theory of operads that would complement any library on the subject. It has a calculational flavor that sets it apart from other texts, and this makes it accessible to both graduate and strong undergraduate students.
-- Nick Gurski, Jahresbericht der Deutschen Mathematiker-Vereinigung
Yau's monograph offers a very careful introduction to the theory of operads that would complement any library on the subject. It has a calculational flavor that sets it apart from other texts, and this makes it accessible to both graduate and strong undergraduate students...it occupies a very interesting space in the operadic literature.
-- Nick Gurski, Jahresbericht der Deutschen Mathematiker-Vereinigung
This book is a useful introduction to colored operads or symmetric multicategories, to the destination of students as well as researchers interested in these objects.
-- Loïc Foissy, Zentralblatt Math
An introductory undergraduate course in abstract algebra is sufficient as a prerequisite for almost all of the material covered in the book. One impressive feature of the book is the emphasis on motivating new concepts as they are introduced and providing numerous graphical illustrations to clarify their geometric significance; there are also numerous exercises collected at the ends of the chapters. The author also provides a list of references to related literature to assist the reader who wishes to continue the study of operads beyond the topics covered in this book.
-- Murray R. Bremner, Mathematical Reviews
The book contains much valuable information and detail, which can potentially save a struggling newcomer into operad land many hours of frustration.
-- Ittay Weiss, MAA Reviews
Table of Contents
Table of Contents
Colored Operads
- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface xiii14
- List of notations xxiii24
- Part 1. Graphs and trees 130
- Chapter 1. Directed graphs 332
- Chapter 2. Extra structures on graphs 1948
- Chapter 3. Rooted trees 2958
- Chapter 4. Collapsing an internal edge 4372
- Chapter 5. Grafting of rooted trees 5382
- Chapter 6. Grafting and extra structures 75104
- Part 2. Category theory 87116
- Chapter 7. Basic category theory 89118
- Chapter 8. Symmetric monoidal categories 121150
- Chapter 9. Colored symmetric sequences and objects 141170
- Part 3. Operads and algebras 159188
- Chapter 10. Motivation for colored operads 161190
- Chapter 11. Colored operads 173202
- Chapter 12. Operads in arity 1 203232
- Chapter 13. Algebras over colored operads 215244
- Chapter 14. Examples of algebras 237266
- Chapter 15. Motivation for partial compositions 265294
- Chapter 16. Colored pseudo-operads 275304
- Part 4. Free colored operads 319348
- Chapter 17. Motivation for free colored operads 321350
- Chapter 18. General operadic composition 333362
- Chapter 19. Free colored non-symmetric operads 351380
- Chapter 20. Free colored operads 381410
- Further reading 409438
- Bibliography 413442
- List of main facts 419448
- Index 423452
- Back Cover Back Cover1458