| Hardcover ISBN: | 978-1-4704-2723-8 |
| Product Code: | GSM/170 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-2871-6 |
| Product Code: | GSM/170.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-1-4704-2723-8 |
| eBook: ISBN: | 978-1-4704-2871-6 |
| Product Code: | GSM/170.B |
| List Price: | $220.00 $177.50 |
| MAA Member Price: | $198.00 $159.75 |
| AMS Member Price: | $176.00 $142.00 |
| Hardcover ISBN: | 978-1-4704-2723-8 |
| Product Code: | GSM/170 |
| List Price: | $135.00 |
| MAA Member Price: | $121.50 |
| AMS Member Price: | $108.00 |
| eBook ISBN: | 978-1-4704-2871-6 |
| Product Code: | GSM/170.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-1-4704-2723-8 |
| eBook ISBN: | 978-1-4704-2871-6 |
| Product Code: | GSM/170.B |
| List Price: | $220.00 $177.50 |
| MAA Member Price: | $198.00 $159.75 |
| AMS Member Price: | $176.00 $142.00 |
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Book DetailsGraduate Studies in MathematicsVolume: 170; 2016; 428 ppMSC: Primary 18; 05; 06
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.
ReadershipGraduate students and researchers in mathematics and other sciences where operads and colored operads are used.
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Table of Contents
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Part 1. Graphs and trees
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Chapter 1. Directed graphs
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Chapter 2. Extra structures on graphs
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Chapter 3. Rooted trees
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Chapter 4. Collapsing an internal edge
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Chapter 5. Grafting of rooted trees
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Chapter 6. Grafting and extra structures
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Part 2. Category theory
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Chapter 7. Basic category theory
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Chapter 8. Symmetric monoidal categories
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Chapter 9. Colored symmetric sequences and objects
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Part 3. Operads and algebras
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Chapter 10. Motivation for colored operads
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Chapter 11. Colored operads
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Chapter 12. Operads in arity 1
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Chapter 13. Algebras over colored operads
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Chapter 14. Examples of algebras
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Chapter 15. Motivation for partial compositions
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Chapter 16. Colored pseudo-operads
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Part 4. Free colored operads
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Chapter 17. Motivation for free colored operads
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Chapter 18. General operadic composition
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Chapter 19. Free colored non-symmetric operads
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Chapter 20. Free colored operads
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Further reading
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Additional Material
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Reviews
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'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
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Graduate students and researchers in mathematics and other sciences where operads and colored operads are used.
-
Part 1. Graphs and trees
-
Chapter 1. Directed graphs
-
Chapter 2. Extra structures on graphs
-
Chapter 3. Rooted trees
-
Chapter 4. Collapsing an internal edge
-
Chapter 5. Grafting of rooted trees
-
Chapter 6. Grafting and extra structures
-
Part 2. Category theory
-
Chapter 7. Basic category theory
-
Chapter 8. Symmetric monoidal categories
-
Chapter 9. Colored symmetric sequences and objects
-
Part 3. Operads and algebras
-
Chapter 10. Motivation for colored operads
-
Chapter 11. Colored operads
-
Chapter 12. Operads in arity 1
-
Chapter 13. Algebras over colored operads
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Chapter 14. Examples of algebras
-
Chapter 15. Motivation for partial compositions
-
Chapter 16. Colored pseudo-operads
-
Part 4. Free colored operads
-
Chapter 17. Motivation for free colored operads
-
Chapter 18. General operadic composition
-
Chapter 19. Free colored non-symmetric operads
-
Chapter 20. Free colored operads
-
Further reading
-
'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
